TSTP Solution File: GEO174+3 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO174+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n012.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 02:52:15 EDT 2022
% Result : Theorem 0.78s 1.40s
% Output : Refutation 0.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GEO174+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : bliksem %s
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % DateTime : Sat Jun 18 11:14:38 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.78/1.40 *** allocated 10000 integers for termspace/termends
% 0.78/1.40 *** allocated 10000 integers for clauses
% 0.78/1.40 *** allocated 10000 integers for justifications
% 0.78/1.40 Bliksem 1.12
% 0.78/1.40
% 0.78/1.40
% 0.78/1.40 Automatic Strategy Selection
% 0.78/1.40
% 0.78/1.40
% 0.78/1.40 Clauses:
% 0.78/1.40
% 0.78/1.40 { ! distinct_points( X, X ) }.
% 0.78/1.40 { ! distinct_lines( X, X ) }.
% 0.78/1.40 { ! convergent_lines( X, X ) }.
% 0.78/1.40 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 0.78/1.40 ) }.
% 0.78/1.40 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.78/1.40 }.
% 0.78/1.40 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 0.78/1.40 , Z ) }.
% 0.78/1.40 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 0.78/1.40 , Y ) ) }.
% 0.78/1.40 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 0.78/1.40 , Y ) ) }.
% 0.78/1.40 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.78/1.40 , Y ), X ) }.
% 0.78/1.40 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.78/1.40 , Y ), Y ) }.
% 0.78/1.40 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 0.78/1.40 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 0.78/1.40 apart_point_and_line( Y, T ) }.
% 0.78/1.40 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 0.78/1.40 apart_point_and_line( Z, Y ) }.
% 0.78/1.40 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 0.78/1.40 apart_point_and_line( X, Z ) }.
% 0.78/1.40 { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X,
% 0.78/1.40 Z ) }.
% 0.78/1.40 { ! distinct_lines( X, Y ), convergent_lines( X, Y ) }.
% 0.78/1.40 { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 0.78/1.40 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 0.78/1.40 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 0.78/1.40 apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 0.78/1.40 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.78/1.40 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.78/1.40 , convergent_lines( Y, Z ) }.
% 0.78/1.40 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.78/1.40 , unorthogonal_lines( Y, Z ) }.
% 0.78/1.40 { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 0.78/1.40 { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.78/1.40 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 0.78/1.40 }.
% 0.78/1.40 { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 0.78/1.40 { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 0.78/1.40 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 0.78/1.40 apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ),
% 0.78/1.40 unorthogonal_lines( Y, T ) }.
% 0.78/1.40 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.78/1.40 { alpha2( X, Z ), convergent_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 0.78/1.40 unorthogonal_lines( X, Y ) }.
% 0.78/1.40 { alpha2( X, Z ), unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 0.78/1.40 unorthogonal_lines( X, Y ) }.
% 0.78/1.40 { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 0.78/1.40 { ! alpha2( X, Y ), unorthogonal_lines( Y, X ) }.
% 0.78/1.40 { ! convergent_lines( Y, X ), ! unorthogonal_lines( Y, X ), alpha2( X, Y )
% 0.78/1.40 }.
% 0.78/1.40 { unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ), !
% 0.78/1.40 convergent_lines( X, Y ) }.
% 0.78/1.40 { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line(
% 0.78/1.40 line_connecting( X, Y ) ) }.
% 0.78/1.40 { ! line( X ), ! line( Y ), ! convergent_lines( X, Y ), point(
% 0.78/1.40 intersection_point( X, Y ) ) }.
% 0.78/1.40 { ! line( X ), ! point( Y ), line( parallel_through_point( X, Y ) ) }.
% 0.78/1.40 { ! line( X ), ! point( Y ), line( orthogonal_through_point( X, Y ) ) }.
% 0.78/1.40 { ! equal_points( X, Y ), ! distinct_points( X, Y ) }.
% 0.78/1.40 { distinct_points( X, Y ), equal_points( X, Y ) }.
% 0.78/1.40 { ! equal_lines( X, Y ), ! distinct_lines( X, Y ) }.
% 0.78/1.40 { distinct_lines( X, Y ), equal_lines( X, Y ) }.
% 0.78/1.40 { ! parallel_lines( X, Y ), ! convergent_lines( X, Y ) }.
% 0.78/1.40 { convergent_lines( X, Y ), parallel_lines( X, Y ) }.
% 0.78/1.40 { ! incident_point_and_line( X, Y ), ! apart_point_and_line( X, Y ) }.
% 0.78/1.40 { apart_point_and_line( X, Y ), incident_point_and_line( X, Y ) }.
% 0.78/1.40 { ! orthogonal_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.78/1.40 { unorthogonal_lines( X, Y ), orthogonal_lines( X, Y ) }.
% 0.78/1.40 { distinct_points( skol1, skol2 ) }.
% 0.78/1.40 { convergent_lines( skol3, skol4 ) }.
% 0.78/1.40 { apart_point_and_line( skol1, skol3 ), apart_point_and_line( skol2, skol3
% 0.78/1.40 ) }.
% 0.78/1.40 { ! distinct_lines( skol3, line_connecting( skol1, skol2 ) ) }.
% 0.78/1.40
% 0.78/1.40 percentage equality = 0.000000, percentage horn = 0.600000
% 0.78/1.40 This a non-horn, non-equality problem
% 0.78/1.40
% 0.78/1.40
% 0.78/1.40 Options Used:
% 0.78/1.40
% 0.78/1.40 useres = 1
% 0.78/1.40 useparamod = 0
% 0.78/1.40 useeqrefl = 0
% 0.78/1.40 useeqfact = 0
% 0.78/1.40 usefactor = 1
% 0.78/1.40 usesimpsplitting = 0
% 0.78/1.40 usesimpdemod = 0
% 0.78/1.40 usesimpres = 3
% 0.78/1.40
% 0.78/1.40 resimpinuse = 1000
% 0.78/1.40 resimpclauses = 20000
% 0.78/1.40 substype = standard
% 0.78/1.40 backwardsubs = 1
% 0.78/1.40 selectoldest = 5
% 0.78/1.40
% 0.78/1.40 litorderings [0] = split
% 0.78/1.40 litorderings [1] = liftord
% 0.78/1.40
% 0.78/1.40 termordering = none
% 0.78/1.40
% 0.78/1.40 litapriori = 1
% 0.78/1.40 termapriori = 0
% 0.78/1.40 litaposteriori = 0
% 0.78/1.40 termaposteriori = 0
% 0.78/1.40 demodaposteriori = 0
% 0.78/1.40 ordereqreflfact = 0
% 0.78/1.40
% 0.78/1.40 litselect = none
% 0.78/1.40
% 0.78/1.40 maxweight = 15
% 0.78/1.40 maxdepth = 30000
% 0.78/1.40 maxlength = 115
% 0.78/1.40 maxnrvars = 195
% 0.78/1.40 excuselevel = 1
% 0.78/1.40 increasemaxweight = 1
% 0.78/1.40
% 0.78/1.40 maxselected = 10000000
% 0.78/1.40 maxnrclauses = 10000000
% 0.78/1.40
% 0.78/1.40 showgenerated = 0
% 0.78/1.40 showkept = 0
% 0.78/1.40 showselected = 0
% 0.78/1.40 showdeleted = 0
% 0.78/1.40 showresimp = 1
% 0.78/1.40 showstatus = 2000
% 0.78/1.40
% 0.78/1.40 prologoutput = 0
% 0.78/1.40 nrgoals = 5000000
% 0.78/1.40 totalproof = 1
% 0.78/1.40
% 0.78/1.40 Symbols occurring in the translation:
% 0.78/1.40
% 0.78/1.40 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.78/1.40 . [1, 2] (w:1, o:27, a:1, s:1, b:0),
% 0.78/1.40 ! [4, 1] (w:0, o:20, a:1, s:1, b:0),
% 0.78/1.40 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.78/1.40 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.78/1.40 distinct_points [36, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.78/1.40 distinct_lines [37, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.78/1.40 convergent_lines [38, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.78/1.40 line_connecting [41, 2] (w:1, o:54, a:1, s:1, b:0),
% 0.78/1.40 apart_point_and_line [42, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.78/1.40 intersection_point [43, 2] (w:1, o:56, a:1, s:1, b:0),
% 0.78/1.40 parallel_through_point [46, 2] (w:1, o:59, a:1, s:1, b:0),
% 0.78/1.40 unorthogonal_lines [49, 2] (w:1, o:60, a:1, s:1, b:0),
% 0.78/1.40 orthogonal_through_point [52, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.78/1.40 point [54, 1] (w:1, o:25, a:1, s:1, b:0),
% 0.78/1.40 line [55, 1] (w:1, o:26, a:1, s:1, b:0),
% 0.78/1.40 equal_points [56, 2] (w:1, o:61, a:1, s:1, b:0),
% 0.78/1.40 equal_lines [57, 2] (w:1, o:62, a:1, s:1, b:0),
% 0.78/1.40 parallel_lines [58, 2] (w:1, o:63, a:1, s:1, b:0),
% 0.78/1.40 incident_point_and_line [59, 2] (w:1, o:64, a:1, s:1, b:0),
% 0.78/1.40 orthogonal_lines [60, 2] (w:1, o:58, a:1, s:1, b:0),
% 0.78/1.40 alpha1 [61, 2] (w:1, o:65, a:1, s:1, b:0),
% 0.78/1.40 alpha2 [62, 2] (w:1, o:66, a:1, s:1, b:0),
% 0.78/1.40 skol1 [63, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.78/1.40 skol2 [64, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.78/1.40 skol3 [65, 0] (w:1, o:18, a:1, s:1, b:0),
% 0.78/1.40 skol4 [66, 0] (w:1, o:19, a:1, s:1, b:0).
% 0.78/1.40
% 0.78/1.40
% 0.78/1.40 Starting Search:
% 0.78/1.40
% 0.78/1.40 *** allocated 15000 integers for clauses
% 0.78/1.40 *** allocated 22500 integers for clauses
% 0.78/1.40 *** allocated 33750 integers for clauses
% 0.78/1.40 *** allocated 15000 integers for termspace/termends
% 0.78/1.40 *** allocated 50625 integers for clauses
% 0.78/1.40 Resimplifying inuse:
% 0.78/1.40 Done
% 0.78/1.40
% 0.78/1.40 *** allocated 22500 integers for termspace/termends
% 0.78/1.40 *** allocated 75937 integers for clauses
% 0.78/1.40 *** allocated 33750 integers for termspace/termends
% 0.78/1.40 *** allocated 113905 integers for clauses
% 0.78/1.40
% 0.78/1.40 Intermediate Status:
% 0.78/1.40 Generated: 10656
% 0.78/1.40 Kept: 2012
% 0.78/1.40 Inuse: 323
% 0.78/1.40 Deleted: 1
% 0.78/1.40 Deletedinuse: 0
% 0.78/1.40
% 0.78/1.40 Resimplifying inuse:
% 0.78/1.40 Done
% 0.78/1.40
% 0.78/1.40 *** allocated 50625 integers for termspace/termends
% 0.78/1.40 *** allocated 170857 integers for clauses
% 0.78/1.40 Resimplifying inuse:
% 0.78/1.40 Done
% 0.78/1.40
% 0.78/1.40
% 0.78/1.40 Bliksems!, er is een bewijs:
% 0.78/1.40 % SZS status Theorem
% 0.78/1.40 % SZS output start Refutation
% 0.78/1.40
% 0.78/1.40 (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.78/1.40 (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.78/1.40 (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.78/1.40 , ! distinct_lines( X, Y ) }.
% 0.78/1.40 (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), convergent_lines( Y,
% 0.78/1.40 Z ), ! convergent_lines( X, Y ) }.
% 0.78/1.40 (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), apart_point_and_line(
% 0.78/1.40 X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.78/1.40 (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ), convergent_lines(
% 0.78/1.40 X, Z ), distinct_lines( Y, Z ) }.
% 0.78/1.40 (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! distinct_lines( X
% 0.78/1.40 , Y ) }.
% 0.78/1.40 (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines( parallel_through_point( Y
% 0.78/1.40 , X ), Y ) }.
% 0.78/1.40 (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.78/1.40 parallel_through_point( Y, X ) ) }.
% 0.78/1.40 (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), unorthogonal_lines(
% 0.78/1.40 X, Y ) }.
% 0.78/1.40 (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 0.78/1.40 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 0.78/1.40 }.
% 0.78/1.40 (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! alpha1( X, Y ) }.
% 0.78/1.40 (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( orthogonal_through_point
% 0.78/1.40 ( Y, X ), Y ) }.
% 0.78/1.40 (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.78/1.40 orthogonal_through_point( Y, X ) ) }.
% 0.78/1.40 (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ), unorthogonal_lines
% 0.78/1.40 ( Z, X ), unorthogonal_lines( Z, Y ) }.
% 0.78/1.40 (48) {G0,W6,D2,L2,V0,M1} I { apart_point_and_line( skol1, skol3 ),
% 0.78/1.40 apart_point_and_line( skol2, skol3 ) }.
% 0.78/1.40 (49) {G0,W5,D3,L1,V0,M1} I { ! distinct_lines( skol3, line_connecting(
% 0.78/1.40 skol1, skol2 ) ) }.
% 0.78/1.40 (56) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 0.78/1.40 ( X, Y ) }.
% 0.78/1.40 (57) {G1,W8,D3,L2,V1,M2} R(49,4) { ! distinct_lines( skol3, X ),
% 0.78/1.40 distinct_lines( X, line_connecting( skol1, skol2 ) ) }.
% 0.78/1.40 (69) {G1,W8,D3,L2,V3,M2} R(5,15) { ! convergent_lines(
% 0.78/1.40 parallel_through_point( Y, Z ), X ), convergent_lines( X, Y ) }.
% 0.78/1.40 (70) {G1,W8,D3,L2,V3,M2} R(5,15) { ! convergent_lines( X,
% 0.78/1.40 parallel_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 0.78/1.40 (72) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.78/1.40 convergent_lines( X, Y ) }.
% 0.78/1.40 (75) {G2,W5,D3,L1,V2,M1} R(72,15) { ! convergent_lines( X,
% 0.78/1.40 parallel_through_point( X, Y ) ) }.
% 0.78/1.40 (77) {G3,W8,D3,L2,V3,M2} R(75,5) { ! convergent_lines( Y, X ),
% 0.78/1.40 convergent_lines( X, parallel_through_point( Y, Z ) ) }.
% 0.78/1.40 (81) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 0.78/1.40 orthogonal_through_point( X, Y ), X ) }.
% 0.78/1.40 (109) {G2,W8,D3,L2,V3,M2} R(81,5) { convergent_lines( X, Z ),
% 0.78/1.40 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.78/1.40 (110) {G2,W6,D2,L2,V2,M1} R(14,56) { convergent_lines( X, Y ), !
% 0.78/1.40 distinct_lines( Y, X ) }.
% 0.78/1.40 (131) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ),
% 0.78/1.40 distinct_lines( Y, T ), apart_point_and_line( Z, T ), !
% 0.78/1.40 apart_point_and_line( Z, X ) }.
% 0.78/1.40 (141) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X,
% 0.78/1.40 parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.78/1.40 (142) {G1,W8,D3,L2,V3,M1} R(12,24) { distinct_lines( X,
% 0.78/1.40 orthogonal_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.78/1.40 (171) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y ),
% 0.78/1.40 convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 0.78/1.40 unorthogonal_lines( Y, Z ) }.
% 0.78/1.40 (177) {G3,W8,D3,L2,V3,M2} R(109,72) { convergent_lines( Z, X ),
% 0.78/1.40 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.78/1.40 (192) {G4,W8,D3,L2,V3,M2} R(177,72) { convergent_lines( X,
% 0.78/1.40 orthogonal_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 0.78/1.40 (226) {G4,W7,D4,L1,V3,M1} R(77,15) { ! convergent_lines( X,
% 0.78/1.40 parallel_through_point( parallel_through_point( X, Y ), Z ) ) }.
% 0.78/1.40 (236) {G5,W7,D4,L1,V3,M1} R(226,72) { ! convergent_lines(
% 0.78/1.40 parallel_through_point( parallel_through_point( X, Y ), Z ), X ) }.
% 0.78/1.40 (240) {G6,W9,D5,L1,V4,M1} R(236,77) { ! convergent_lines( X,
% 0.78/1.40 parallel_through_point( parallel_through_point( parallel_through_point( X
% 0.78/1.40 , Y ), Z ), T ) ) }.
% 0.78/1.40 (280) {G1,W8,D3,L2,V3,M1} R(31,23) { ! convergent_lines( X, Y ),
% 0.78/1.40 unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 0.78/1.40 (303) {G2,W8,D3,L2,V3,M2} R(69,72) { convergent_lines( X, Z ), !
% 0.78/1.40 convergent_lines( parallel_through_point( X, Y ), Z ) }.
% 0.78/1.40 (314) {G3,W8,D3,L2,V3,M2} R(303,72) { ! convergent_lines( Y,
% 0.78/1.40 parallel_through_point( X, Z ) ), convergent_lines( X, Y ) }.
% 0.78/1.40 (543) {G2,W8,D3,L2,V1,M1} R(57,14) { convergent_lines( X, line_connecting(
% 0.78/1.40 skol1, skol2 ) ), ! distinct_lines( skol3, X ) }.
% 0.78/1.40 (569) {G3,W11,D3,L3,V2,M2} R(543,13) { ! convergent_lines( Y, skol3 ),
% 0.78/1.40 convergent_lines( Y, X ), convergent_lines( X, line_connecting( skol1,
% 0.78/1.40 skol2 ) ) }.
% 0.78/1.40 (573) {G4,W5,D3,L1,V0,M1} F(569);r(2) { ! convergent_lines( line_connecting
% 0.78/1.40 ( skol1, skol2 ), skol3 ) }.
% 0.78/1.40 (575) {G5,W7,D4,L1,V1,M1} R(573,314) { ! convergent_lines( skol3,
% 0.78/1.40 parallel_through_point( line_connecting( skol1, skol2 ), X ) ) }.
% 0.78/1.40 (619) {G6,W9,D5,L1,V2,M1} R(575,70) { ! convergent_lines( skol3,
% 0.78/1.40 parallel_through_point( parallel_through_point( line_connecting( skol1,
% 0.78/1.40 skol2 ), X ), Y ) ) }.
% 0.78/1.40 (2605) {G2,W14,D3,L4,V5,M1} R(131,142) { distinct_lines( X, Y ),
% 0.78/1.40 distinct_lines( Y, Z ), distinct_lines( Z, orthogonal_through_point( U, T
% 0.78/1.40 ) ), ! apart_point_and_line( T, X ) }.
% 0.78/1.40 (2606) {G2,W14,D3,L4,V5,M1} R(131,141) { distinct_lines( X, Y ),
% 0.78/1.40 distinct_lines( Y, Z ), distinct_lines( Z, parallel_through_point( U, T )
% 0.78/1.40 ), ! apart_point_and_line( T, X ) }.
% 0.78/1.40 (2614) {G3,W8,D3,L2,V3,M1} F(2606);r(56) { distinct_lines(
% 0.78/1.40 parallel_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.78/1.40 (2615) {G3,W8,D3,L2,V3,M1} F(2605);r(56) { distinct_lines(
% 0.78/1.40 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.78/1.40 (2631) {G4,W8,D3,L2,V1,M1} R(2615,48) { distinct_lines(
% 0.78/1.40 orthogonal_through_point( X, skol2 ), skol3 ), apart_point_and_line(
% 0.78/1.40 skol1, skol3 ) }.
% 0.78/1.40 (2660) {G5,W10,D3,L2,V2,M1} R(2631,2614) { distinct_lines(
% 0.78/1.40 orthogonal_through_point( X, skol2 ), skol3 ), distinct_lines(
% 0.78/1.40 parallel_through_point( Y, skol1 ), skol3 ) }.
% 0.78/1.40 (2925) {G6,W10,D3,L2,V2,M1} R(2660,110) { convergent_lines( skol3,
% 0.78/1.40 parallel_through_point( Y, skol1 ) ), distinct_lines(
% 0.78/1.40 orthogonal_through_point( X, skol2 ), skol3 ) }.
% 0.78/1.40 (2950) {G7,W10,D3,L2,V2,M1} R(2925,110) { convergent_lines( skol3,
% 0.78/1.40 orthogonal_through_point( Y, skol2 ) ), convergent_lines( skol3,
% 0.78/1.40 parallel_through_point( X, skol1 ) ) }.
% 0.78/1.40 (2968) {G8,W5,D3,L1,V1,M1} R(2950,619) { convergent_lines( skol3,
% 0.78/1.40 orthogonal_through_point( X, skol2 ) ) }.
% 0.78/1.40 (2982) {G9,W5,D3,L1,V1,M1} R(2968,72) { convergent_lines(
% 0.78/1.40 orthogonal_through_point( X, skol2 ), skol3 ) }.
% 0.78/1.40 (3469) {G5,W8,D3,L2,V3,M1} R(171,23);r(192) { convergent_lines( X, Y ), !
% 0.78/1.40 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 0.78/1.40 (3476) {G6,W10,D3,L2,V4,M2} R(3469,280) { ! convergent_lines(
% 0.78/1.40 orthogonal_through_point( Z, T ), X ), convergent_lines(
% 0.78/1.40 orthogonal_through_point( X, Y ), Z ) }.
% 0.78/1.40 (3500) {G10,W5,D3,L1,V2,M1} R(3476,2982) { convergent_lines(
% 0.78/1.40 orthogonal_through_point( skol3, X ), Y ) }.
% 0.78/1.40 (3585) {G11,W0,D0,L0,V0,M0} R(3500,240) { }.
% 0.78/1.40
% 0.78/1.40
% 0.78/1.40 % SZS output end Refutation
% 0.78/1.40 found a proof!
% 0.78/1.40
% 0.78/1.40
% 0.78/1.40 Unprocessed initial clauses:
% 0.78/1.40
% 0.78/1.40 (3587) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 0.78/1.40 (3588) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.78/1.40 (3589) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 0.78/1.40 (3590) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 0.78/1.40 , Z ), distinct_points( Y, Z ) }.
% 0.78/1.40 (3591) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X,
% 0.78/1.40 Z ), distinct_lines( Y, Z ) }.
% 0.78/1.40 (3592) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines
% 0.78/1.40 ( X, Z ), convergent_lines( Y, Z ) }.
% 0.78/1.40 (3593) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.78/1.40 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 0.78/1.40 (3594) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.78/1.40 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 0.78/1.40 (3595) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 0.78/1.40 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 0.78/1.40 (3596) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 0.78/1.40 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 0.78/1.40 (3597) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines
% 0.78/1.40 ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 0.78/1.40 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 0.78/1.40 (3598) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 0.78/1.40 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 0.78/1.40 (3599) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 0.78/1.40 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 0.78/1.40 (3600) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), distinct_lines( Y
% 0.78/1.40 , Z ), convergent_lines( X, Z ) }.
% 0.78/1.40 (3601) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ), convergent_lines( X
% 0.78/1.40 , Y ) }.
% 0.78/1.40 (3602) {G0,W5,D3,L1,V2,M1} { ! convergent_lines( parallel_through_point( Y
% 0.78/1.40 , X ), Y ) }.
% 0.78/1.40 (3603) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.78/1.40 parallel_through_point( Y, X ) ) }.
% 0.78/1.40 (3604) {G0,W12,D2,L4,V3,M4} { ! distinct_lines( X, Y ),
% 0.78/1.40 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 0.78/1.40 convergent_lines( X, Y ) }.
% 0.78/1.40 (3605) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines
% 0.78/1.40 ( X, Y ) }.
% 0.78/1.40 (3606) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.78/1.40 unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 0.78/1.40 (3607) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.78/1.40 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 0.78/1.40 }.
% 0.78/1.40 (3608) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines( X, Y )
% 0.78/1.40 }.
% 0.78/1.40 (3609) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 0.78/1.40 }.
% 0.78/1.40 (3610) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( X, Y ), !
% 0.78/1.40 unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 0.78/1.40 (3611) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines(
% 0.78/1.40 orthogonal_through_point( Y, X ), Y ) }.
% 0.78/1.40 (3612) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.78/1.40 orthogonal_through_point( Y, X ) ) }.
% 0.78/1.40 (3613) {G0,W15,D2,L5,V4,M5} { ! distinct_lines( X, Y ),
% 0.78/1.40 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 0.78/1.40 unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 0.78/1.40 (3614) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines
% 0.78/1.40 ( X, Y ) }.
% 0.78/1.40 (3615) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), convergent_lines( Z, Y ), !
% 0.78/1.40 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.78/1.40 (3616) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), unorthogonal_lines( Z, Y ),
% 0.78/1.40 ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.78/1.40 (3617) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), convergent_lines( Y, X )
% 0.78/1.40 }.
% 0.78/1.40 (3618) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), unorthogonal_lines( Y, X )
% 0.78/1.40 }.
% 0.78/1.40 (3619) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( Y, X ), !
% 0.78/1.40 unorthogonal_lines( Y, X ), alpha2( X, Y ) }.
% 0.78/1.40 (3620) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ),
% 0.78/1.40 unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 0.78/1.40 (3621) {G0,W11,D3,L4,V2,M4} { ! point( X ), ! point( Y ), !
% 0.78/1.40 distinct_points( X, Y ), line( line_connecting( X, Y ) ) }.
% 0.78/1.40 (3622) {G0,W11,D3,L4,V2,M4} { ! line( X ), ! line( Y ), ! convergent_lines
% 0.78/1.40 ( X, Y ), point( intersection_point( X, Y ) ) }.
% 0.78/1.40 (3623) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 0.78/1.40 parallel_through_point( X, Y ) ) }.
% 0.78/1.40 (3624) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 0.78/1.40 orthogonal_through_point( X, Y ) ) }.
% 0.78/1.40 (3625) {G0,W6,D2,L2,V2,M2} { ! equal_points( X, Y ), ! distinct_points( X
% 0.78/1.40 , Y ) }.
% 0.78/1.40 (3626) {G0,W6,D2,L2,V2,M2} { distinct_points( X, Y ), equal_points( X, Y )
% 0.78/1.40 }.
% 0.78/1.40 (3627) {G0,W6,D2,L2,V2,M2} { ! equal_lines( X, Y ), ! distinct_lines( X, Y
% 0.78/1.40 ) }.
% 0.78/1.40 (3628) {G0,W6,D2,L2,V2,M2} { distinct_lines( X, Y ), equal_lines( X, Y )
% 0.78/1.40 }.
% 0.78/1.40 (3629) {G0,W6,D2,L2,V2,M2} { ! parallel_lines( X, Y ), ! convergent_lines
% 0.78/1.40 ( X, Y ) }.
% 0.78/1.40 (3630) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), parallel_lines( X,
% 0.78/1.40 Y ) }.
% 0.78/1.40 (3631) {G0,W6,D2,L2,V2,M2} { ! incident_point_and_line( X, Y ), !
% 0.78/1.40 apart_point_and_line( X, Y ) }.
% 0.78/1.40 (3632) {G0,W6,D2,L2,V2,M2} { apart_point_and_line( X, Y ),
% 0.78/1.40 incident_point_and_line( X, Y ) }.
% 0.78/1.40 (3633) {G0,W6,D2,L2,V2,M2} { ! orthogonal_lines( X, Y ), !
% 0.78/1.40 unorthogonal_lines( X, Y ) }.
% 0.78/1.40 (3634) {G0,W6,D2,L2,V2,M2} { unorthogonal_lines( X, Y ), orthogonal_lines
% 0.78/1.40 ( X, Y ) }.
% 0.78/1.40 (3635) {G0,W3,D2,L1,V0,M1} { distinct_points( skol1, skol2 ) }.
% 0.78/1.40 (3636) {G0,W3,D2,L1,V0,M1} { convergent_lines( skol3, skol4 ) }.
% 0.78/1.40 (3637) {G0,W6,D2,L2,V0,M2} { apart_point_and_line( skol1, skol3 ),
% 0.78/1.40 apart_point_and_line( skol2, skol3 ) }.
% 0.78/1.40 (3638) {G0,W5,D3,L1,V0,M1} { ! distinct_lines( skol3, line_connecting(
% 0.78/1.40 skol1, skol2 ) ) }.
% 0.78/1.40
% 0.78/1.40
% 0.78/1.40 Total Proof:
% 0.78/1.40
% 0.78/1.40 subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.78/1.40 parent0: (3588) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := X
% 0.78/1.40 end
% 0.78/1.40 permutation0:
% 0.78/1.40 0 ==> 0
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 subsumption: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.78/1.40 parent0: (3589) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := X
% 0.78/1.40 end
% 0.78/1.40 permutation0:
% 0.78/1.40 0 ==> 0
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 0.78/1.40 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 0.78/1.40 parent0: (3591) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ),
% 0.78/1.40 distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := X
% 0.78/1.40 Y := Y
% 0.78/1.40 Z := Z
% 0.78/1.40 end
% 0.78/1.40 permutation0:
% 0.78/1.40 0 ==> 2
% 0.78/1.40 1 ==> 0
% 0.78/1.40 2 ==> 1
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 subsumption: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 0.78/1.40 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.78/1.40 parent0: (3592) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 0.78/1.40 convergent_lines( X, Z ), convergent_lines( Y, Z ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := X
% 0.78/1.40 Y := Y
% 0.78/1.40 Z := Z
% 0.78/1.40 end
% 0.78/1.40 permutation0:
% 0.78/1.40 0 ==> 2
% 0.78/1.40 1 ==> 0
% 0.78/1.40 2 ==> 1
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 subsumption: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 0.78/1.40 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.78/1.40 parent0: (3599) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 0.78/1.40 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := X
% 0.78/1.40 Y := Y
% 0.78/1.40 Z := Z
% 0.78/1.40 end
% 0.78/1.40 permutation0:
% 0.78/1.40 0 ==> 2
% 0.78/1.40 1 ==> 0
% 0.78/1.40 2 ==> 1
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 subsumption: (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ),
% 0.78/1.40 convergent_lines( X, Z ), distinct_lines( Y, Z ) }.
% 0.78/1.40 parent0: (3600) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 0.78/1.40 distinct_lines( Y, Z ), convergent_lines( X, Z ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := X
% 0.78/1.40 Y := Y
% 0.78/1.40 Z := Z
% 0.78/1.40 end
% 0.78/1.40 permutation0:
% 0.78/1.40 0 ==> 0
% 0.78/1.40 1 ==> 2
% 0.78/1.40 2 ==> 1
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 subsumption: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 0.78/1.40 distinct_lines( X, Y ) }.
% 0.78/1.40 parent0: (3601) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ),
% 0.78/1.40 convergent_lines( X, Y ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := X
% 0.78/1.40 Y := Y
% 0.78/1.40 end
% 0.78/1.40 permutation0:
% 0.78/1.40 0 ==> 1
% 0.78/1.40 1 ==> 0
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 subsumption: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 0.78/1.40 parallel_through_point( Y, X ), Y ) }.
% 0.78/1.40 parent0: (3602) {G0,W5,D3,L1,V2,M1} { ! convergent_lines(
% 0.78/1.40 parallel_through_point( Y, X ), Y ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := X
% 0.78/1.40 Y := Y
% 0.78/1.40 end
% 0.78/1.40 permutation0:
% 0.78/1.40 0 ==> 0
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 subsumption: (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.78/1.40 parallel_through_point( Y, X ) ) }.
% 0.78/1.40 parent0: (3603) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.78/1.40 parallel_through_point( Y, X ) ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := X
% 0.78/1.40 Y := Y
% 0.78/1.40 end
% 0.78/1.40 permutation0:
% 0.78/1.40 0 ==> 0
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 subsumption: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 0.78/1.40 unorthogonal_lines( X, Y ) }.
% 0.78/1.40 parent0: (3605) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ),
% 0.78/1.40 unorthogonal_lines( X, Y ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := X
% 0.78/1.40 Y := Y
% 0.78/1.40 end
% 0.78/1.40 permutation0:
% 0.78/1.40 0 ==> 0
% 0.78/1.40 1 ==> 1
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 subsumption: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 0.78/1.40 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 0.78/1.40 }.
% 0.78/1.40 parent0: (3607) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.78/1.40 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 0.78/1.40 }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := X
% 0.78/1.40 Y := Y
% 0.78/1.40 Z := Z
% 0.78/1.40 end
% 0.78/1.40 permutation0:
% 0.78/1.40 0 ==> 0
% 0.78/1.40 1 ==> 1
% 0.78/1.40 2 ==> 3
% 0.78/1.40 3 ==> 2
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 subsumption: (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 0.78/1.40 alpha1( X, Y ) }.
% 0.78/1.40 parent0: (3608) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines(
% 0.78/1.40 X, Y ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := X
% 0.78/1.40 Y := Y
% 0.78/1.40 end
% 0.78/1.40 permutation0:
% 0.78/1.40 0 ==> 1
% 0.78/1.40 1 ==> 0
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 subsumption: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 0.78/1.40 orthogonal_through_point( Y, X ), Y ) }.
% 0.78/1.40 parent0: (3611) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines(
% 0.78/1.40 orthogonal_through_point( Y, X ), Y ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := X
% 0.78/1.40 Y := Y
% 0.78/1.40 end
% 0.78/1.40 permutation0:
% 0.78/1.40 0 ==> 0
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 subsumption: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.78/1.40 orthogonal_through_point( Y, X ) ) }.
% 0.78/1.40 parent0: (3612) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.78/1.40 orthogonal_through_point( Y, X ) ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := X
% 0.78/1.40 Y := Y
% 0.78/1.40 end
% 0.78/1.40 permutation0:
% 0.78/1.40 0 ==> 0
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 subsumption: (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ),
% 0.78/1.40 unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ) }.
% 0.78/1.40 parent0: (3620) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ),
% 0.78/1.40 unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := X
% 0.78/1.40 Y := Y
% 0.78/1.40 Z := Z
% 0.78/1.40 end
% 0.78/1.40 permutation0:
% 0.78/1.40 0 ==> 1
% 0.78/1.40 1 ==> 2
% 0.78/1.40 2 ==> 0
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 subsumption: (48) {G0,W6,D2,L2,V0,M1} I { apart_point_and_line( skol1,
% 0.78/1.40 skol3 ), apart_point_and_line( skol2, skol3 ) }.
% 0.78/1.40 parent0: (3637) {G0,W6,D2,L2,V0,M2} { apart_point_and_line( skol1, skol3 )
% 0.78/1.40 , apart_point_and_line( skol2, skol3 ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 end
% 0.78/1.40 permutation0:
% 0.78/1.40 0 ==> 0
% 0.78/1.40 1 ==> 1
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 subsumption: (49) {G0,W5,D3,L1,V0,M1} I { ! distinct_lines( skol3,
% 0.78/1.40 line_connecting( skol1, skol2 ) ) }.
% 0.78/1.40 parent0: (3638) {G0,W5,D3,L1,V0,M1} { ! distinct_lines( skol3,
% 0.78/1.40 line_connecting( skol1, skol2 ) ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 end
% 0.78/1.40 permutation0:
% 0.78/1.40 0 ==> 0
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 resolution: (3782) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 0.78/1.40 distinct_lines( X, Y ) }.
% 0.78/1.40 parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.78/1.40 parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 0.78/1.40 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := X
% 0.78/1.40 end
% 0.78/1.40 substitution1:
% 0.78/1.40 X := X
% 0.78/1.40 Y := Y
% 0.78/1.40 Z := X
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 subsumption: (56) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 0.78/1.40 distinct_lines( X, Y ) }.
% 0.78/1.40 parent0: (3782) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 0.78/1.40 distinct_lines( X, Y ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := Y
% 0.78/1.40 Y := X
% 0.78/1.40 end
% 0.78/1.40 permutation0:
% 0.78/1.40 0 ==> 1
% 0.78/1.40 1 ==> 0
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 resolution: (3784) {G1,W8,D3,L2,V1,M2} { distinct_lines( X,
% 0.78/1.40 line_connecting( skol1, skol2 ) ), ! distinct_lines( skol3, X ) }.
% 0.78/1.40 parent0[0]: (49) {G0,W5,D3,L1,V0,M1} I { ! distinct_lines( skol3,
% 0.78/1.40 line_connecting( skol1, skol2 ) ) }.
% 0.78/1.40 parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 0.78/1.40 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 end
% 0.78/1.40 substitution1:
% 0.78/1.40 X := skol3
% 0.78/1.40 Y := X
% 0.78/1.40 Z := line_connecting( skol1, skol2 )
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 subsumption: (57) {G1,W8,D3,L2,V1,M2} R(49,4) { ! distinct_lines( skol3, X
% 0.78/1.40 ), distinct_lines( X, line_connecting( skol1, skol2 ) ) }.
% 0.78/1.40 parent0: (3784) {G1,W8,D3,L2,V1,M2} { distinct_lines( X, line_connecting(
% 0.78/1.40 skol1, skol2 ) ), ! distinct_lines( skol3, X ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := X
% 0.78/1.40 end
% 0.78/1.40 permutation0:
% 0.78/1.40 0 ==> 1
% 0.78/1.40 1 ==> 0
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 resolution: (3786) {G1,W8,D3,L2,V3,M2} { convergent_lines( Z, X ), !
% 0.78/1.40 convergent_lines( parallel_through_point( X, Y ), Z ) }.
% 0.78/1.40 parent0[0]: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 0.78/1.40 parallel_through_point( Y, X ), Y ) }.
% 0.78/1.40 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 0.78/1.40 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := Y
% 0.78/1.40 Y := X
% 0.78/1.40 end
% 0.78/1.40 substitution1:
% 0.78/1.40 X := parallel_through_point( X, Y )
% 0.78/1.40 Y := Z
% 0.78/1.40 Z := X
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 subsumption: (69) {G1,W8,D3,L2,V3,M2} R(5,15) { ! convergent_lines(
% 0.78/1.40 parallel_through_point( Y, Z ), X ), convergent_lines( X, Y ) }.
% 0.78/1.40 parent0: (3786) {G1,W8,D3,L2,V3,M2} { convergent_lines( Z, X ), !
% 0.78/1.40 convergent_lines( parallel_through_point( X, Y ), Z ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := Y
% 0.78/1.40 Y := Z
% 0.78/1.40 Z := X
% 0.78/1.40 end
% 0.78/1.40 permutation0:
% 0.78/1.40 0 ==> 1
% 0.78/1.40 1 ==> 0
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 resolution: (3789) {G1,W8,D3,L2,V3,M2} { convergent_lines( Z, X ), !
% 0.78/1.40 convergent_lines( Z, parallel_through_point( X, Y ) ) }.
% 0.78/1.40 parent0[0]: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 0.78/1.40 parallel_through_point( Y, X ), Y ) }.
% 0.78/1.40 parent1[1]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 0.78/1.40 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := Y
% 0.78/1.40 Y := X
% 0.78/1.40 end
% 0.78/1.40 substitution1:
% 0.78/1.40 X := Z
% 0.78/1.40 Y := parallel_through_point( X, Y )
% 0.78/1.40 Z := X
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 subsumption: (70) {G1,W8,D3,L2,V3,M2} R(5,15) { ! convergent_lines( X,
% 0.78/1.40 parallel_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 0.78/1.40 parent0: (3789) {G1,W8,D3,L2,V3,M2} { convergent_lines( Z, X ), !
% 0.78/1.40 convergent_lines( Z, parallel_through_point( X, Y ) ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := Y
% 0.78/1.40 Y := Z
% 0.78/1.40 Z := X
% 0.78/1.40 end
% 0.78/1.40 permutation0:
% 0.78/1.40 0 ==> 1
% 0.78/1.40 1 ==> 0
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 resolution: (3790) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 0.78/1.40 convergent_lines( X, Y ) }.
% 0.78/1.40 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.78/1.40 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 0.78/1.40 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := X
% 0.78/1.40 end
% 0.78/1.40 substitution1:
% 0.78/1.40 X := X
% 0.78/1.40 Y := Y
% 0.78/1.40 Z := X
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 subsumption: (72) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.78/1.40 convergent_lines( X, Y ) }.
% 0.78/1.40 parent0: (3790) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 0.78/1.40 convergent_lines( X, Y ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := Y
% 0.78/1.40 Y := X
% 0.78/1.40 end
% 0.78/1.40 permutation0:
% 0.78/1.40 0 ==> 1
% 0.78/1.40 1 ==> 0
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 resolution: (3792) {G1,W5,D3,L1,V2,M1} { ! convergent_lines( X,
% 0.78/1.40 parallel_through_point( X, Y ) ) }.
% 0.78/1.40 parent0[0]: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 0.78/1.40 parallel_through_point( Y, X ), Y ) }.
% 0.78/1.40 parent1[1]: (72) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.78/1.40 convergent_lines( X, Y ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := Y
% 0.78/1.40 Y := X
% 0.78/1.40 end
% 0.78/1.40 substitution1:
% 0.78/1.40 X := parallel_through_point( X, Y )
% 0.78/1.40 Y := X
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 subsumption: (75) {G2,W5,D3,L1,V2,M1} R(72,15) { ! convergent_lines( X,
% 0.78/1.40 parallel_through_point( X, Y ) ) }.
% 0.78/1.40 parent0: (3792) {G1,W5,D3,L1,V2,M1} { ! convergent_lines( X,
% 0.78/1.40 parallel_through_point( X, Y ) ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := X
% 0.78/1.40 Y := Y
% 0.78/1.40 end
% 0.78/1.40 permutation0:
% 0.78/1.40 0 ==> 0
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 resolution: (3793) {G1,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 0.78/1.40 parallel_through_point( X, Y ) ), ! convergent_lines( X, Z ) }.
% 0.78/1.40 parent0[0]: (75) {G2,W5,D3,L1,V2,M1} R(72,15) { ! convergent_lines( X,
% 0.78/1.40 parallel_through_point( X, Y ) ) }.
% 0.78/1.40 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 0.78/1.40 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := X
% 0.78/1.40 Y := Y
% 0.78/1.40 end
% 0.78/1.40 substitution1:
% 0.78/1.40 X := X
% 0.78/1.40 Y := Z
% 0.78/1.40 Z := parallel_through_point( X, Y )
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 subsumption: (77) {G3,W8,D3,L2,V3,M2} R(75,5) { ! convergent_lines( Y, X )
% 0.78/1.40 , convergent_lines( X, parallel_through_point( Y, Z ) ) }.
% 0.78/1.40 parent0: (3793) {G1,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 0.78/1.40 parallel_through_point( X, Y ) ), ! convergent_lines( X, Z ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := Y
% 0.78/1.40 Y := Z
% 0.78/1.40 Z := X
% 0.78/1.40 end
% 0.78/1.40 permutation0:
% 0.78/1.40 0 ==> 1
% 0.78/1.40 1 ==> 0
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 resolution: (3795) {G1,W5,D3,L1,V2,M1} { convergent_lines(
% 0.78/1.40 orthogonal_through_point( X, Y ), X ) }.
% 0.78/1.40 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 0.78/1.40 orthogonal_through_point( Y, X ), Y ) }.
% 0.78/1.40 parent1[1]: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 0.78/1.40 unorthogonal_lines( X, Y ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := Y
% 0.78/1.40 Y := X
% 0.78/1.40 end
% 0.78/1.40 substitution1:
% 0.78/1.40 X := orthogonal_through_point( X, Y )
% 0.78/1.40 Y := X
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 subsumption: (81) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 0.78/1.40 orthogonal_through_point( X, Y ), X ) }.
% 0.78/1.40 parent0: (3795) {G1,W5,D3,L1,V2,M1} { convergent_lines(
% 0.78/1.40 orthogonal_through_point( X, Y ), X ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := X
% 0.78/1.40 Y := Y
% 0.78/1.40 end
% 0.78/1.40 permutation0:
% 0.78/1.40 0 ==> 0
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 resolution: (3796) {G1,W8,D3,L2,V3,M2} { convergent_lines(
% 0.78/1.40 orthogonal_through_point( X, Y ), Z ), convergent_lines( X, Z ) }.
% 0.78/1.40 parent0[2]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 0.78/1.40 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.78/1.40 parent1[0]: (81) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 0.78/1.40 orthogonal_through_point( X, Y ), X ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := orthogonal_through_point( X, Y )
% 0.78/1.40 Y := X
% 0.78/1.40 Z := Z
% 0.78/1.40 end
% 0.78/1.40 substitution1:
% 0.78/1.40 X := X
% 0.78/1.40 Y := Y
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 subsumption: (109) {G2,W8,D3,L2,V3,M2} R(81,5) { convergent_lines( X, Z ),
% 0.78/1.40 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.78/1.40 parent0: (3796) {G1,W8,D3,L2,V3,M2} { convergent_lines(
% 0.78/1.40 orthogonal_through_point( X, Y ), Z ), convergent_lines( X, Z ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := X
% 0.78/1.40 Y := Y
% 0.78/1.40 Z := Z
% 0.78/1.40 end
% 0.78/1.40 permutation0:
% 0.78/1.40 0 ==> 1
% 0.78/1.40 1 ==> 0
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 resolution: (3797) {G1,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), !
% 0.78/1.40 distinct_lines( Y, X ) }.
% 0.78/1.40 parent0[1]: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 0.78/1.40 distinct_lines( X, Y ) }.
% 0.78/1.40 parent1[1]: (56) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 0.78/1.40 distinct_lines( X, Y ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := X
% 0.78/1.40 Y := Y
% 0.78/1.40 end
% 0.78/1.40 substitution1:
% 0.78/1.40 X := X
% 0.78/1.40 Y := Y
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 subsumption: (110) {G2,W6,D2,L2,V2,M1} R(14,56) { convergent_lines( X, Y )
% 0.78/1.40 , ! distinct_lines( Y, X ) }.
% 0.78/1.40 parent0: (3797) {G1,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), !
% 0.78/1.40 distinct_lines( Y, X ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := X
% 0.78/1.40 Y := Y
% 0.78/1.40 end
% 0.78/1.40 permutation0:
% 0.78/1.40 0 ==> 0
% 0.78/1.40 1 ==> 1
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 resolution: (3798) {G1,W12,D2,L4,V4,M4} { distinct_lines( X, Y ),
% 0.78/1.40 apart_point_and_line( Z, Y ), distinct_lines( T, X ), !
% 0.78/1.40 apart_point_and_line( Z, T ) }.
% 0.78/1.40 parent0[2]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 0.78/1.40 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.78/1.40 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 0.78/1.40 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := Z
% 0.78/1.40 Y := X
% 0.78/1.40 Z := Y
% 0.78/1.40 end
% 0.78/1.40 substitution1:
% 0.78/1.40 X := Z
% 0.78/1.40 Y := T
% 0.78/1.40 Z := X
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 subsumption: (131) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ),
% 0.78/1.40 distinct_lines( Y, T ), apart_point_and_line( Z, T ), !
% 0.78/1.40 apart_point_and_line( Z, X ) }.
% 0.78/1.40 parent0: (3798) {G1,W12,D2,L4,V4,M4} { distinct_lines( X, Y ),
% 0.78/1.40 apart_point_and_line( Z, Y ), distinct_lines( T, X ), !
% 0.78/1.40 apart_point_and_line( Z, T ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := Y
% 0.78/1.40 Y := T
% 0.78/1.40 Z := Z
% 0.78/1.40 T := X
% 0.78/1.40 end
% 0.78/1.40 permutation0:
% 0.78/1.40 0 ==> 1
% 0.78/1.40 1 ==> 2
% 0.78/1.40 2 ==> 0
% 0.78/1.40 3 ==> 3
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 resolution: (3800) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 0.78/1.40 parallel_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 0.78/1.40 parent0[0]: (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.78/1.40 parallel_through_point( Y, X ) ) }.
% 0.78/1.40 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 0.78/1.40 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := X
% 0.78/1.40 Y := Y
% 0.78/1.40 end
% 0.78/1.40 substitution1:
% 0.78/1.40 X := X
% 0.78/1.40 Y := Z
% 0.78/1.40 Z := parallel_through_point( Y, X )
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 subsumption: (141) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X,
% 0.78/1.40 parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.78/1.40 parent0: (3800) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 0.78/1.40 parallel_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := Z
% 0.78/1.40 Y := Y
% 0.78/1.40 Z := X
% 0.78/1.40 end
% 0.78/1.40 permutation0:
% 0.78/1.40 0 ==> 0
% 0.78/1.40 1 ==> 1
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 resolution: (3801) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 0.78/1.40 orthogonal_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 0.78/1.40 parent0[0]: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.78/1.40 orthogonal_through_point( Y, X ) ) }.
% 0.78/1.40 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 0.78/1.40 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := X
% 0.78/1.40 Y := Y
% 0.78/1.40 end
% 0.78/1.40 substitution1:
% 0.78/1.40 X := X
% 0.78/1.40 Y := Z
% 0.78/1.40 Z := orthogonal_through_point( Y, X )
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 subsumption: (142) {G1,W8,D3,L2,V3,M1} R(12,24) { distinct_lines( X,
% 0.78/1.40 orthogonal_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.78/1.40 parent0: (3801) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 0.78/1.40 orthogonal_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := Z
% 0.78/1.40 Y := Y
% 0.78/1.40 Z := X
% 0.78/1.40 end
% 0.78/1.40 permutation0:
% 0.78/1.40 0 ==> 0
% 0.78/1.40 1 ==> 1
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 resolution: (3803) {G1,W12,D2,L4,V3,M4} { convergent_lines( X, Y ), !
% 0.78/1.40 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ),
% 0.78/1.40 unorthogonal_lines( Z, Y ) }.
% 0.78/1.40 parent0[1]: (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! alpha1
% 0.78/1.40 ( X, Y ) }.
% 0.78/1.40 parent1[3]: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 0.78/1.40 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 0.78/1.40 }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := X
% 0.78/1.40 Y := Y
% 0.78/1.40 end
% 0.78/1.40 substitution1:
% 0.78/1.40 X := X
% 0.78/1.40 Y := Z
% 0.78/1.40 Z := Y
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 subsumption: (171) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y
% 0.78/1.40 ), convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 0.78/1.40 unorthogonal_lines( Y, Z ) }.
% 0.78/1.40 parent0: (3803) {G1,W12,D2,L4,V3,M4} { convergent_lines( X, Y ), !
% 0.78/1.40 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ),
% 0.78/1.40 unorthogonal_lines( Z, Y ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := X
% 0.78/1.40 Y := Z
% 0.78/1.40 Z := Y
% 0.78/1.40 end
% 0.78/1.40 permutation0:
% 0.78/1.40 0 ==> 1
% 0.78/1.40 1 ==> 0
% 0.78/1.40 2 ==> 2
% 0.78/1.40 3 ==> 3
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 resolution: (3804) {G2,W8,D3,L2,V3,M2} { convergent_lines( Y, X ),
% 0.78/1.40 convergent_lines( orthogonal_through_point( X, Z ), Y ) }.
% 0.78/1.40 parent0[0]: (72) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.78/1.40 convergent_lines( X, Y ) }.
% 0.78/1.40 parent1[0]: (109) {G2,W8,D3,L2,V3,M2} R(81,5) { convergent_lines( X, Z ),
% 0.78/1.40 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := Y
% 0.78/1.40 Y := X
% 0.78/1.40 end
% 0.78/1.40 substitution1:
% 0.78/1.40 X := X
% 0.78/1.40 Y := Z
% 0.78/1.40 Z := Y
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 subsumption: (177) {G3,W8,D3,L2,V3,M2} R(109,72) { convergent_lines( Z, X )
% 0.78/1.40 , convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.78/1.40 parent0: (3804) {G2,W8,D3,L2,V3,M2} { convergent_lines( Y, X ),
% 0.78/1.40 convergent_lines( orthogonal_through_point( X, Z ), Y ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := X
% 0.78/1.40 Y := Z
% 0.78/1.40 Z := Y
% 0.78/1.40 end
% 0.78/1.40 permutation0:
% 0.78/1.40 0 ==> 0
% 0.78/1.40 1 ==> 1
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 resolution: (3807) {G2,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 0.78/1.40 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ) }.
% 0.78/1.40 parent0[0]: (72) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.78/1.40 convergent_lines( X, Y ) }.
% 0.78/1.40 parent1[1]: (177) {G3,W8,D3,L2,V3,M2} R(109,72) { convergent_lines( Z, X )
% 0.78/1.40 , convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := Z
% 0.78/1.40 Y := orthogonal_through_point( X, Y )
% 0.78/1.40 end
% 0.78/1.40 substitution1:
% 0.78/1.40 X := X
% 0.78/1.40 Y := Y
% 0.78/1.40 Z := Z
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 subsumption: (192) {G4,W8,D3,L2,V3,M2} R(177,72) { convergent_lines( X,
% 0.78/1.40 orthogonal_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 0.78/1.40 parent0: (3807) {G2,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 0.78/1.40 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ) }.
% 0.78/1.40 substitution0:
% 0.78/1.40 X := Y
% 0.78/1.40 Y := Z
% 0.78/1.40 Z := X
% 0.78/1.40 end
% 0.78/1.40 permutation0:
% 0.78/1.40 0 ==> 0
% 0.78/1.40 1 ==> 1
% 0.78/1.40 end
% 0.78/1.40
% 0.78/1.40 resolution: (3808) {G1,W7,D4,L1,V3,M1} { ! convergent_lines( X,
% 0.78/1.41 parallel_through_point( parallel_through_point( X, Y ), Z ) ) }.
% 0.78/1.41 parent0[0]: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 0.78/1.41 parallel_through_point( Y, X ), Y ) }.
% 0.78/1.41 parent1[1]: (77) {G3,W8,D3,L2,V3,M2} R(75,5) { ! convergent_lines( Y, X ),
% 0.78/1.41 convergent_lines( X, parallel_through_point( Y, Z ) ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := Z
% 0.78/1.41 Y := parallel_through_point( X, Y )
% 0.78/1.41 end
% 0.78/1.41 substitution1:
% 0.78/1.41 X := parallel_through_point( parallel_through_point( X, Y ), Z )
% 0.78/1.41 Y := X
% 0.78/1.41 Z := Y
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 subsumption: (226) {G4,W7,D4,L1,V3,M1} R(77,15) { ! convergent_lines( X,
% 0.78/1.41 parallel_through_point( parallel_through_point( X, Y ), Z ) ) }.
% 0.78/1.41 parent0: (3808) {G1,W7,D4,L1,V3,M1} { ! convergent_lines( X,
% 0.78/1.41 parallel_through_point( parallel_through_point( X, Y ), Z ) ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := X
% 0.78/1.41 Y := Y
% 0.78/1.41 Z := Z
% 0.78/1.41 end
% 0.78/1.41 permutation0:
% 0.78/1.41 0 ==> 0
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 resolution: (3809) {G2,W7,D4,L1,V3,M1} { ! convergent_lines(
% 0.78/1.41 parallel_through_point( parallel_through_point( X, Y ), Z ), X ) }.
% 0.78/1.41 parent0[0]: (226) {G4,W7,D4,L1,V3,M1} R(77,15) { ! convergent_lines( X,
% 0.78/1.41 parallel_through_point( parallel_through_point( X, Y ), Z ) ) }.
% 0.78/1.41 parent1[1]: (72) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.78/1.41 convergent_lines( X, Y ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := X
% 0.78/1.41 Y := Y
% 0.78/1.41 Z := Z
% 0.78/1.41 end
% 0.78/1.41 substitution1:
% 0.78/1.41 X := X
% 0.78/1.41 Y := parallel_through_point( parallel_through_point( X, Y ), Z )
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 subsumption: (236) {G5,W7,D4,L1,V3,M1} R(226,72) { ! convergent_lines(
% 0.78/1.41 parallel_through_point( parallel_through_point( X, Y ), Z ), X ) }.
% 0.78/1.41 parent0: (3809) {G2,W7,D4,L1,V3,M1} { ! convergent_lines(
% 0.78/1.41 parallel_through_point( parallel_through_point( X, Y ), Z ), X ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := X
% 0.78/1.41 Y := Y
% 0.78/1.41 Z := Z
% 0.78/1.41 end
% 0.78/1.41 permutation0:
% 0.78/1.41 0 ==> 0
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 resolution: (3810) {G4,W9,D5,L1,V4,M1} { ! convergent_lines( X,
% 0.78/1.41 parallel_through_point( parallel_through_point( parallel_through_point( X
% 0.78/1.41 , Y ), Z ), T ) ) }.
% 0.78/1.41 parent0[0]: (236) {G5,W7,D4,L1,V3,M1} R(226,72) { ! convergent_lines(
% 0.78/1.41 parallel_through_point( parallel_through_point( X, Y ), Z ), X ) }.
% 0.78/1.41 parent1[1]: (77) {G3,W8,D3,L2,V3,M2} R(75,5) { ! convergent_lines( Y, X ),
% 0.78/1.41 convergent_lines( X, parallel_through_point( Y, Z ) ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := parallel_through_point( X, Y )
% 0.78/1.41 Y := Z
% 0.78/1.41 Z := T
% 0.78/1.41 end
% 0.78/1.41 substitution1:
% 0.78/1.41 X := parallel_through_point( parallel_through_point(
% 0.78/1.41 parallel_through_point( X, Y ), Z ), T )
% 0.78/1.41 Y := X
% 0.78/1.41 Z := Y
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 subsumption: (240) {G6,W9,D5,L1,V4,M1} R(236,77) { ! convergent_lines( X,
% 0.78/1.41 parallel_through_point( parallel_through_point( parallel_through_point( X
% 0.78/1.41 , Y ), Z ), T ) ) }.
% 0.78/1.41 parent0: (3810) {G4,W9,D5,L1,V4,M1} { ! convergent_lines( X,
% 0.78/1.41 parallel_through_point( parallel_through_point( parallel_through_point( X
% 0.78/1.41 , Y ), Z ), T ) ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := X
% 0.78/1.41 Y := Y
% 0.78/1.41 Z := Z
% 0.78/1.41 T := T
% 0.78/1.41 end
% 0.78/1.41 permutation0:
% 0.78/1.41 0 ==> 0
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 resolution: (3812) {G1,W8,D3,L2,V3,M2} { ! convergent_lines( Z, X ),
% 0.78/1.41 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.78/1.41 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 0.78/1.41 orthogonal_through_point( Y, X ), Y ) }.
% 0.78/1.41 parent1[2]: (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ),
% 0.78/1.41 unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := Y
% 0.78/1.41 Y := X
% 0.78/1.41 end
% 0.78/1.41 substitution1:
% 0.78/1.41 X := Z
% 0.78/1.41 Y := X
% 0.78/1.41 Z := orthogonal_through_point( X, Y )
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 subsumption: (280) {G1,W8,D3,L2,V3,M1} R(31,23) { ! convergent_lines( X, Y
% 0.78/1.41 ), unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 0.78/1.41 parent0: (3812) {G1,W8,D3,L2,V3,M2} { ! convergent_lines( Z, X ),
% 0.78/1.41 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := Y
% 0.78/1.41 Y := Z
% 0.78/1.41 Z := X
% 0.78/1.41 end
% 0.78/1.41 permutation0:
% 0.78/1.41 0 ==> 0
% 0.78/1.41 1 ==> 1
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 resolution: (3814) {G2,W8,D3,L2,V3,M2} { convergent_lines( Y, X ), !
% 0.78/1.41 convergent_lines( parallel_through_point( Y, Z ), X ) }.
% 0.78/1.41 parent0[0]: (72) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.78/1.41 convergent_lines( X, Y ) }.
% 0.78/1.41 parent1[1]: (69) {G1,W8,D3,L2,V3,M2} R(5,15) { ! convergent_lines(
% 0.78/1.41 parallel_through_point( Y, Z ), X ), convergent_lines( X, Y ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := Y
% 0.78/1.41 Y := X
% 0.78/1.41 end
% 0.78/1.41 substitution1:
% 0.78/1.41 X := X
% 0.78/1.41 Y := Y
% 0.78/1.41 Z := Z
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 subsumption: (303) {G2,W8,D3,L2,V3,M2} R(69,72) { convergent_lines( X, Z )
% 0.78/1.41 , ! convergent_lines( parallel_through_point( X, Y ), Z ) }.
% 0.78/1.41 parent0: (3814) {G2,W8,D3,L2,V3,M2} { convergent_lines( Y, X ), !
% 0.78/1.41 convergent_lines( parallel_through_point( Y, Z ), X ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := Z
% 0.78/1.41 Y := X
% 0.78/1.41 Z := Y
% 0.78/1.41 end
% 0.78/1.41 permutation0:
% 0.78/1.41 0 ==> 0
% 0.78/1.41 1 ==> 1
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 resolution: (3815) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 0.78/1.41 convergent_lines( Y, parallel_through_point( X, Z ) ) }.
% 0.78/1.41 parent0[1]: (303) {G2,W8,D3,L2,V3,M2} R(69,72) { convergent_lines( X, Z ),
% 0.78/1.41 ! convergent_lines( parallel_through_point( X, Y ), Z ) }.
% 0.78/1.41 parent1[1]: (72) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.78/1.41 convergent_lines( X, Y ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := X
% 0.78/1.41 Y := Z
% 0.78/1.41 Z := Y
% 0.78/1.41 end
% 0.78/1.41 substitution1:
% 0.78/1.41 X := parallel_through_point( X, Z )
% 0.78/1.41 Y := Y
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 subsumption: (314) {G3,W8,D3,L2,V3,M2} R(303,72) { ! convergent_lines( Y,
% 0.78/1.41 parallel_through_point( X, Z ) ), convergent_lines( X, Y ) }.
% 0.78/1.41 parent0: (3815) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 0.78/1.41 convergent_lines( Y, parallel_through_point( X, Z ) ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := X
% 0.78/1.41 Y := Y
% 0.78/1.41 Z := Z
% 0.78/1.41 end
% 0.78/1.41 permutation0:
% 0.78/1.41 0 ==> 1
% 0.78/1.41 1 ==> 0
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 resolution: (3816) {G1,W8,D3,L2,V1,M2} { convergent_lines( X,
% 0.78/1.41 line_connecting( skol1, skol2 ) ), ! distinct_lines( skol3, X ) }.
% 0.78/1.41 parent0[1]: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 0.78/1.41 distinct_lines( X, Y ) }.
% 0.78/1.41 parent1[1]: (57) {G1,W8,D3,L2,V1,M2} R(49,4) { ! distinct_lines( skol3, X )
% 0.78/1.41 , distinct_lines( X, line_connecting( skol1, skol2 ) ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := X
% 0.78/1.41 Y := line_connecting( skol1, skol2 )
% 0.78/1.41 end
% 0.78/1.41 substitution1:
% 0.78/1.41 X := X
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 subsumption: (543) {G2,W8,D3,L2,V1,M1} R(57,14) { convergent_lines( X,
% 0.78/1.41 line_connecting( skol1, skol2 ) ), ! distinct_lines( skol3, X ) }.
% 0.78/1.41 parent0: (3816) {G1,W8,D3,L2,V1,M2} { convergent_lines( X, line_connecting
% 0.78/1.41 ( skol1, skol2 ) ), ! distinct_lines( skol3, X ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := X
% 0.78/1.41 end
% 0.78/1.41 permutation0:
% 0.78/1.41 0 ==> 0
% 0.78/1.41 1 ==> 1
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 resolution: (3817) {G1,W11,D3,L3,V2,M3} { convergent_lines( X,
% 0.78/1.41 line_connecting( skol1, skol2 ) ), ! convergent_lines( Y, skol3 ),
% 0.78/1.41 convergent_lines( Y, X ) }.
% 0.78/1.41 parent0[1]: (543) {G2,W8,D3,L2,V1,M1} R(57,14) { convergent_lines( X,
% 0.78/1.41 line_connecting( skol1, skol2 ) ), ! distinct_lines( skol3, X ) }.
% 0.78/1.41 parent1[2]: (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ),
% 0.78/1.41 convergent_lines( X, Z ), distinct_lines( Y, Z ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := X
% 0.78/1.41 end
% 0.78/1.41 substitution1:
% 0.78/1.41 X := Y
% 0.78/1.41 Y := skol3
% 0.78/1.41 Z := X
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 subsumption: (569) {G3,W11,D3,L3,V2,M2} R(543,13) { ! convergent_lines( Y,
% 0.78/1.41 skol3 ), convergent_lines( Y, X ), convergent_lines( X, line_connecting(
% 0.78/1.41 skol1, skol2 ) ) }.
% 0.78/1.41 parent0: (3817) {G1,W11,D3,L3,V2,M3} { convergent_lines( X,
% 0.78/1.41 line_connecting( skol1, skol2 ) ), ! convergent_lines( Y, skol3 ),
% 0.78/1.41 convergent_lines( Y, X ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := X
% 0.78/1.41 Y := Y
% 0.78/1.41 end
% 0.78/1.41 permutation0:
% 0.78/1.41 0 ==> 2
% 0.78/1.41 1 ==> 0
% 0.78/1.41 2 ==> 1
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 factor: (3819) {G3,W12,D3,L2,V0,M2} { ! convergent_lines( line_connecting
% 0.78/1.41 ( skol1, skol2 ), skol3 ), convergent_lines( line_connecting( skol1,
% 0.78/1.41 skol2 ), line_connecting( skol1, skol2 ) ) }.
% 0.78/1.41 parent0[1, 2]: (569) {G3,W11,D3,L3,V2,M2} R(543,13) { ! convergent_lines( Y
% 0.78/1.41 , skol3 ), convergent_lines( Y, X ), convergent_lines( X, line_connecting
% 0.78/1.41 ( skol1, skol2 ) ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := line_connecting( skol1, skol2 )
% 0.78/1.41 Y := line_connecting( skol1, skol2 )
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 resolution: (3820) {G1,W5,D3,L1,V0,M1} { ! convergent_lines(
% 0.78/1.41 line_connecting( skol1, skol2 ), skol3 ) }.
% 0.78/1.41 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.78/1.41 parent1[1]: (3819) {G3,W12,D3,L2,V0,M2} { ! convergent_lines(
% 0.78/1.41 line_connecting( skol1, skol2 ), skol3 ), convergent_lines(
% 0.78/1.41 line_connecting( skol1, skol2 ), line_connecting( skol1, skol2 ) ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := line_connecting( skol1, skol2 )
% 0.78/1.41 end
% 0.78/1.41 substitution1:
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 subsumption: (573) {G4,W5,D3,L1,V0,M1} F(569);r(2) { ! convergent_lines(
% 0.78/1.41 line_connecting( skol1, skol2 ), skol3 ) }.
% 0.78/1.41 parent0: (3820) {G1,W5,D3,L1,V0,M1} { ! convergent_lines( line_connecting
% 0.78/1.41 ( skol1, skol2 ), skol3 ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 end
% 0.78/1.41 permutation0:
% 0.78/1.41 0 ==> 0
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 resolution: (3821) {G4,W7,D4,L1,V1,M1} { ! convergent_lines( skol3,
% 0.78/1.41 parallel_through_point( line_connecting( skol1, skol2 ), X ) ) }.
% 0.78/1.41 parent0[0]: (573) {G4,W5,D3,L1,V0,M1} F(569);r(2) { ! convergent_lines(
% 0.78/1.41 line_connecting( skol1, skol2 ), skol3 ) }.
% 0.78/1.41 parent1[1]: (314) {G3,W8,D3,L2,V3,M2} R(303,72) { ! convergent_lines( Y,
% 0.78/1.41 parallel_through_point( X, Z ) ), convergent_lines( X, Y ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 end
% 0.78/1.41 substitution1:
% 0.78/1.41 X := line_connecting( skol1, skol2 )
% 0.78/1.41 Y := skol3
% 0.78/1.41 Z := X
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 subsumption: (575) {G5,W7,D4,L1,V1,M1} R(573,314) { ! convergent_lines(
% 0.78/1.41 skol3, parallel_through_point( line_connecting( skol1, skol2 ), X ) ) }.
% 0.78/1.41 parent0: (3821) {G4,W7,D4,L1,V1,M1} { ! convergent_lines( skol3,
% 0.78/1.41 parallel_through_point( line_connecting( skol1, skol2 ), X ) ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := X
% 0.78/1.41 end
% 0.78/1.41 permutation0:
% 0.78/1.41 0 ==> 0
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 resolution: (3822) {G2,W9,D5,L1,V2,M1} { ! convergent_lines( skol3,
% 0.78/1.41 parallel_through_point( parallel_through_point( line_connecting( skol1,
% 0.78/1.41 skol2 ), X ), Y ) ) }.
% 0.78/1.41 parent0[0]: (575) {G5,W7,D4,L1,V1,M1} R(573,314) { ! convergent_lines(
% 0.78/1.41 skol3, parallel_through_point( line_connecting( skol1, skol2 ), X ) ) }.
% 0.78/1.41 parent1[1]: (70) {G1,W8,D3,L2,V3,M2} R(5,15) { ! convergent_lines( X,
% 0.78/1.41 parallel_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := X
% 0.78/1.41 end
% 0.78/1.41 substitution1:
% 0.78/1.41 X := skol3
% 0.78/1.41 Y := parallel_through_point( line_connecting( skol1, skol2 ), X )
% 0.78/1.41 Z := Y
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 subsumption: (619) {G6,W9,D5,L1,V2,M1} R(575,70) { ! convergent_lines(
% 0.78/1.41 skol3, parallel_through_point( parallel_through_point( line_connecting(
% 0.78/1.41 skol1, skol2 ), X ), Y ) ) }.
% 0.78/1.41 parent0: (3822) {G2,W9,D5,L1,V2,M1} { ! convergent_lines( skol3,
% 0.78/1.41 parallel_through_point( parallel_through_point( line_connecting( skol1,
% 0.78/1.41 skol2 ), X ), Y ) ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := X
% 0.78/1.41 Y := Y
% 0.78/1.41 end
% 0.78/1.41 permutation0:
% 0.78/1.41 0 ==> 0
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 resolution: (3823) {G2,W14,D3,L4,V5,M4} { distinct_lines( X,
% 0.78/1.41 orthogonal_through_point( Y, Z ) ), distinct_lines( T, U ),
% 0.78/1.41 distinct_lines( U, X ), ! apart_point_and_line( Z, T ) }.
% 0.78/1.41 parent0[1]: (142) {G1,W8,D3,L2,V3,M1} R(12,24) { distinct_lines( X,
% 0.78/1.41 orthogonal_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.78/1.41 parent1[2]: (131) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ),
% 0.78/1.41 distinct_lines( Y, T ), apart_point_and_line( Z, T ), !
% 0.78/1.41 apart_point_and_line( Z, X ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := X
% 0.78/1.41 Y := Y
% 0.78/1.41 Z := Z
% 0.78/1.41 end
% 0.78/1.41 substitution1:
% 0.78/1.41 X := T
% 0.78/1.41 Y := U
% 0.78/1.41 Z := Z
% 0.78/1.41 T := X
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 subsumption: (2605) {G2,W14,D3,L4,V5,M1} R(131,142) { distinct_lines( X, Y
% 0.78/1.41 ), distinct_lines( Y, Z ), distinct_lines( Z, orthogonal_through_point(
% 0.78/1.41 U, T ) ), ! apart_point_and_line( T, X ) }.
% 0.78/1.41 parent0: (3823) {G2,W14,D3,L4,V5,M4} { distinct_lines( X,
% 0.78/1.41 orthogonal_through_point( Y, Z ) ), distinct_lines( T, U ),
% 0.78/1.41 distinct_lines( U, X ), ! apart_point_and_line( Z, T ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := Z
% 0.78/1.41 Y := U
% 0.78/1.41 Z := T
% 0.78/1.41 T := X
% 0.78/1.41 U := Y
% 0.78/1.41 end
% 0.78/1.41 permutation0:
% 0.78/1.41 0 ==> 2
% 0.78/1.41 1 ==> 0
% 0.78/1.41 2 ==> 1
% 0.78/1.41 3 ==> 3
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 resolution: (3828) {G2,W14,D3,L4,V5,M4} { distinct_lines( X,
% 0.78/1.41 parallel_through_point( Y, Z ) ), distinct_lines( T, U ), distinct_lines
% 0.78/1.41 ( U, X ), ! apart_point_and_line( Z, T ) }.
% 0.78/1.41 parent0[1]: (141) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X,
% 0.78/1.41 parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.78/1.41 parent1[2]: (131) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ),
% 0.78/1.41 distinct_lines( Y, T ), apart_point_and_line( Z, T ), !
% 0.78/1.41 apart_point_and_line( Z, X ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := X
% 0.78/1.41 Y := Y
% 0.78/1.41 Z := Z
% 0.78/1.41 end
% 0.78/1.41 substitution1:
% 0.78/1.41 X := T
% 0.78/1.41 Y := U
% 0.78/1.41 Z := Z
% 0.78/1.41 T := X
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 subsumption: (2606) {G2,W14,D3,L4,V5,M1} R(131,141) { distinct_lines( X, Y
% 0.78/1.41 ), distinct_lines( Y, Z ), distinct_lines( Z, parallel_through_point( U
% 0.78/1.41 , T ) ), ! apart_point_and_line( T, X ) }.
% 0.78/1.41 parent0: (3828) {G2,W14,D3,L4,V5,M4} { distinct_lines( X,
% 0.78/1.41 parallel_through_point( Y, Z ) ), distinct_lines( T, U ), distinct_lines
% 0.78/1.41 ( U, X ), ! apart_point_and_line( Z, T ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := Z
% 0.78/1.41 Y := U
% 0.78/1.41 Z := T
% 0.78/1.41 T := X
% 0.78/1.41 U := Y
% 0.78/1.41 end
% 0.78/1.41 permutation0:
% 0.78/1.41 0 ==> 2
% 0.78/1.41 1 ==> 0
% 0.78/1.41 2 ==> 1
% 0.78/1.41 3 ==> 3
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 factor: (3834) {G2,W13,D3,L3,V3,M3} { distinct_lines( X,
% 0.78/1.41 parallel_through_point( Y, Z ) ), distinct_lines( parallel_through_point
% 0.78/1.41 ( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.78/1.41 parent0[0, 2]: (2606) {G2,W14,D3,L4,V5,M1} R(131,141) { distinct_lines( X,
% 0.78/1.41 Y ), distinct_lines( Y, Z ), distinct_lines( Z, parallel_through_point( U
% 0.78/1.41 , T ) ), ! apart_point_and_line( T, X ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := X
% 0.78/1.41 Y := parallel_through_point( Y, Z )
% 0.78/1.41 Z := X
% 0.78/1.41 T := Z
% 0.78/1.41 U := Y
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 resolution: (3840) {G2,W13,D3,L3,V3,M3} { distinct_lines(
% 0.78/1.41 parallel_through_point( Y, Z ), X ), distinct_lines(
% 0.78/1.41 parallel_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.78/1.41 parent0[0]: (56) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 0.78/1.41 distinct_lines( X, Y ) }.
% 0.78/1.41 parent1[0]: (3834) {G2,W13,D3,L3,V3,M3} { distinct_lines( X,
% 0.78/1.41 parallel_through_point( Y, Z ) ), distinct_lines( parallel_through_point
% 0.78/1.41 ( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := parallel_through_point( Y, Z )
% 0.78/1.41 Y := X
% 0.78/1.41 end
% 0.78/1.41 substitution1:
% 0.78/1.41 X := X
% 0.78/1.41 Y := Y
% 0.78/1.41 Z := Z
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 factor: (3842) {G2,W8,D3,L2,V3,M2} { distinct_lines(
% 0.78/1.41 parallel_through_point( X, Y ), Z ), ! apart_point_and_line( Y, Z ) }.
% 0.78/1.41 parent0[0, 1]: (3840) {G2,W13,D3,L3,V3,M3} { distinct_lines(
% 0.78/1.41 parallel_through_point( Y, Z ), X ), distinct_lines(
% 0.78/1.41 parallel_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := Z
% 0.78/1.41 Y := X
% 0.78/1.41 Z := Y
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 subsumption: (2614) {G3,W8,D3,L2,V3,M1} F(2606);r(56) { distinct_lines(
% 0.78/1.41 parallel_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.78/1.41 parent0: (3842) {G2,W8,D3,L2,V3,M2} { distinct_lines(
% 0.78/1.41 parallel_through_point( X, Y ), Z ), ! apart_point_and_line( Y, Z ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := Y
% 0.78/1.41 Y := Z
% 0.78/1.41 Z := X
% 0.78/1.41 end
% 0.78/1.41 permutation0:
% 0.78/1.41 0 ==> 0
% 0.78/1.41 1 ==> 1
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 factor: (3845) {G2,W13,D3,L3,V3,M3} { distinct_lines( X,
% 0.78/1.41 orthogonal_through_point( Y, Z ) ), distinct_lines(
% 0.78/1.41 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.78/1.41 parent0[0, 2]: (2605) {G2,W14,D3,L4,V5,M1} R(131,142) { distinct_lines( X,
% 0.78/1.41 Y ), distinct_lines( Y, Z ), distinct_lines( Z, orthogonal_through_point
% 0.78/1.41 ( U, T ) ), ! apart_point_and_line( T, X ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := X
% 0.78/1.41 Y := orthogonal_through_point( Y, Z )
% 0.78/1.41 Z := X
% 0.78/1.41 T := Z
% 0.78/1.41 U := Y
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 resolution: (3851) {G2,W13,D3,L3,V3,M3} { distinct_lines(
% 0.78/1.41 orthogonal_through_point( Y, Z ), X ), distinct_lines(
% 0.78/1.41 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.78/1.41 parent0[0]: (56) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 0.78/1.41 distinct_lines( X, Y ) }.
% 0.78/1.41 parent1[0]: (3845) {G2,W13,D3,L3,V3,M3} { distinct_lines( X,
% 0.78/1.41 orthogonal_through_point( Y, Z ) ), distinct_lines(
% 0.78/1.41 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := orthogonal_through_point( Y, Z )
% 0.78/1.41 Y := X
% 0.78/1.41 end
% 0.78/1.41 substitution1:
% 0.78/1.41 X := X
% 0.78/1.41 Y := Y
% 0.78/1.41 Z := Z
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 factor: (3853) {G2,W8,D3,L2,V3,M2} { distinct_lines(
% 0.78/1.41 orthogonal_through_point( X, Y ), Z ), ! apart_point_and_line( Y, Z ) }.
% 0.78/1.41 parent0[0, 1]: (3851) {G2,W13,D3,L3,V3,M3} { distinct_lines(
% 0.78/1.41 orthogonal_through_point( Y, Z ), X ), distinct_lines(
% 0.78/1.41 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := Z
% 0.78/1.41 Y := X
% 0.78/1.41 Z := Y
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 subsumption: (2615) {G3,W8,D3,L2,V3,M1} F(2605);r(56) { distinct_lines(
% 0.78/1.41 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.78/1.41 parent0: (3853) {G2,W8,D3,L2,V3,M2} { distinct_lines(
% 0.78/1.41 orthogonal_through_point( X, Y ), Z ), ! apart_point_and_line( Y, Z ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := Y
% 0.78/1.41 Y := Z
% 0.78/1.41 Z := X
% 0.78/1.41 end
% 0.78/1.41 permutation0:
% 0.78/1.41 0 ==> 0
% 0.78/1.41 1 ==> 1
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 resolution: (3856) {G1,W8,D3,L2,V1,M2} { distinct_lines(
% 0.78/1.41 orthogonal_through_point( X, skol2 ), skol3 ), apart_point_and_line(
% 0.78/1.41 skol1, skol3 ) }.
% 0.78/1.41 parent0[1]: (2615) {G3,W8,D3,L2,V3,M1} F(2605);r(56) { distinct_lines(
% 0.78/1.41 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.78/1.41 parent1[1]: (48) {G0,W6,D2,L2,V0,M1} I { apart_point_and_line( skol1, skol3
% 0.78/1.41 ), apart_point_and_line( skol2, skol3 ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := skol3
% 0.78/1.41 Y := X
% 0.78/1.41 Z := skol2
% 0.78/1.41 end
% 0.78/1.41 substitution1:
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 subsumption: (2631) {G4,W8,D3,L2,V1,M1} R(2615,48) { distinct_lines(
% 0.78/1.41 orthogonal_through_point( X, skol2 ), skol3 ), apart_point_and_line(
% 0.78/1.41 skol1, skol3 ) }.
% 0.78/1.41 parent0: (3856) {G1,W8,D3,L2,V1,M2} { distinct_lines(
% 0.78/1.41 orthogonal_through_point( X, skol2 ), skol3 ), apart_point_and_line(
% 0.78/1.41 skol1, skol3 ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := X
% 0.78/1.41 end
% 0.78/1.41 permutation0:
% 0.78/1.41 0 ==> 0
% 0.78/1.41 1 ==> 1
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 resolution: (3857) {G4,W10,D3,L2,V2,M2} { distinct_lines(
% 0.78/1.41 parallel_through_point( X, skol1 ), skol3 ), distinct_lines(
% 0.78/1.41 orthogonal_through_point( Y, skol2 ), skol3 ) }.
% 0.78/1.41 parent0[1]: (2614) {G3,W8,D3,L2,V3,M1} F(2606);r(56) { distinct_lines(
% 0.78/1.41 parallel_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.78/1.41 parent1[1]: (2631) {G4,W8,D3,L2,V1,M1} R(2615,48) { distinct_lines(
% 0.78/1.41 orthogonal_through_point( X, skol2 ), skol3 ), apart_point_and_line(
% 0.78/1.41 skol1, skol3 ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := skol3
% 0.78/1.41 Y := X
% 0.78/1.41 Z := skol1
% 0.78/1.41 end
% 0.78/1.41 substitution1:
% 0.78/1.41 X := Y
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 subsumption: (2660) {G5,W10,D3,L2,V2,M1} R(2631,2614) { distinct_lines(
% 0.78/1.41 orthogonal_through_point( X, skol2 ), skol3 ), distinct_lines(
% 0.78/1.41 parallel_through_point( Y, skol1 ), skol3 ) }.
% 0.78/1.41 parent0: (3857) {G4,W10,D3,L2,V2,M2} { distinct_lines(
% 0.78/1.41 parallel_through_point( X, skol1 ), skol3 ), distinct_lines(
% 0.78/1.41 orthogonal_through_point( Y, skol2 ), skol3 ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := Y
% 0.78/1.41 Y := X
% 0.78/1.41 end
% 0.78/1.41 permutation0:
% 0.78/1.41 0 ==> 1
% 0.78/1.41 1 ==> 0
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 resolution: (3859) {G3,W10,D3,L2,V2,M2} { convergent_lines( skol3,
% 0.78/1.41 parallel_through_point( X, skol1 ) ), distinct_lines(
% 0.78/1.41 orthogonal_through_point( Y, skol2 ), skol3 ) }.
% 0.78/1.41 parent0[1]: (110) {G2,W6,D2,L2,V2,M1} R(14,56) { convergent_lines( X, Y ),
% 0.78/1.41 ! distinct_lines( Y, X ) }.
% 0.78/1.41 parent1[1]: (2660) {G5,W10,D3,L2,V2,M1} R(2631,2614) { distinct_lines(
% 0.78/1.41 orthogonal_through_point( X, skol2 ), skol3 ), distinct_lines(
% 0.78/1.41 parallel_through_point( Y, skol1 ), skol3 ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := skol3
% 0.78/1.41 Y := parallel_through_point( X, skol1 )
% 0.78/1.41 end
% 0.78/1.41 substitution1:
% 0.78/1.41 X := Y
% 0.78/1.41 Y := X
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 subsumption: (2925) {G6,W10,D3,L2,V2,M1} R(2660,110) { convergent_lines(
% 0.78/1.41 skol3, parallel_through_point( Y, skol1 ) ), distinct_lines(
% 0.78/1.41 orthogonal_through_point( X, skol2 ), skol3 ) }.
% 0.78/1.41 parent0: (3859) {G3,W10,D3,L2,V2,M2} { convergent_lines( skol3,
% 0.78/1.41 parallel_through_point( X, skol1 ) ), distinct_lines(
% 0.78/1.41 orthogonal_through_point( Y, skol2 ), skol3 ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := Y
% 0.78/1.41 Y := X
% 0.78/1.41 end
% 0.78/1.41 permutation0:
% 0.78/1.41 0 ==> 0
% 0.78/1.41 1 ==> 1
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 resolution: (3860) {G3,W10,D3,L2,V2,M2} { convergent_lines( skol3,
% 0.78/1.41 orthogonal_through_point( X, skol2 ) ), convergent_lines( skol3,
% 0.78/1.41 parallel_through_point( Y, skol1 ) ) }.
% 0.78/1.41 parent0[1]: (110) {G2,W6,D2,L2,V2,M1} R(14,56) { convergent_lines( X, Y ),
% 0.78/1.41 ! distinct_lines( Y, X ) }.
% 0.78/1.41 parent1[1]: (2925) {G6,W10,D3,L2,V2,M1} R(2660,110) { convergent_lines(
% 0.78/1.41 skol3, parallel_through_point( Y, skol1 ) ), distinct_lines(
% 0.78/1.41 orthogonal_through_point( X, skol2 ), skol3 ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := skol3
% 0.78/1.41 Y := orthogonal_through_point( X, skol2 )
% 0.78/1.41 end
% 0.78/1.41 substitution1:
% 0.78/1.41 X := X
% 0.78/1.41 Y := Y
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 subsumption: (2950) {G7,W10,D3,L2,V2,M1} R(2925,110) { convergent_lines(
% 0.78/1.41 skol3, orthogonal_through_point( Y, skol2 ) ), convergent_lines( skol3,
% 0.78/1.41 parallel_through_point( X, skol1 ) ) }.
% 0.78/1.41 parent0: (3860) {G3,W10,D3,L2,V2,M2} { convergent_lines( skol3,
% 0.78/1.41 orthogonal_through_point( X, skol2 ) ), convergent_lines( skol3,
% 0.78/1.41 parallel_through_point( Y, skol1 ) ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := Y
% 0.78/1.41 Y := X
% 0.78/1.41 end
% 0.78/1.41 permutation0:
% 0.78/1.41 0 ==> 0
% 0.78/1.41 1 ==> 1
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 resolution: (3861) {G7,W5,D3,L1,V1,M1} { convergent_lines( skol3,
% 0.78/1.41 orthogonal_through_point( Y, skol2 ) ) }.
% 0.78/1.41 parent0[0]: (619) {G6,W9,D5,L1,V2,M1} R(575,70) { ! convergent_lines( skol3
% 0.78/1.41 , parallel_through_point( parallel_through_point( line_connecting( skol1
% 0.78/1.41 , skol2 ), X ), Y ) ) }.
% 0.78/1.41 parent1[1]: (2950) {G7,W10,D3,L2,V2,M1} R(2925,110) { convergent_lines(
% 0.78/1.41 skol3, orthogonal_through_point( Y, skol2 ) ), convergent_lines( skol3,
% 0.78/1.41 parallel_through_point( X, skol1 ) ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := X
% 0.78/1.41 Y := skol1
% 0.78/1.41 end
% 0.78/1.41 substitution1:
% 0.78/1.41 X := parallel_through_point( line_connecting( skol1, skol2 ), X )
% 0.78/1.41 Y := Y
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 subsumption: (2968) {G8,W5,D3,L1,V1,M1} R(2950,619) { convergent_lines(
% 0.78/1.41 skol3, orthogonal_through_point( X, skol2 ) ) }.
% 0.78/1.41 parent0: (3861) {G7,W5,D3,L1,V1,M1} { convergent_lines( skol3,
% 0.78/1.41 orthogonal_through_point( Y, skol2 ) ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := Y
% 0.78/1.41 Y := X
% 0.78/1.41 end
% 0.78/1.41 permutation0:
% 0.78/1.41 0 ==> 0
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 resolution: (3862) {G2,W5,D3,L1,V1,M1} { convergent_lines(
% 0.78/1.41 orthogonal_through_point( X, skol2 ), skol3 ) }.
% 0.78/1.41 parent0[0]: (72) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.78/1.41 convergent_lines( X, Y ) }.
% 0.78/1.41 parent1[0]: (2968) {G8,W5,D3,L1,V1,M1} R(2950,619) { convergent_lines(
% 0.78/1.41 skol3, orthogonal_through_point( X, skol2 ) ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := orthogonal_through_point( X, skol2 )
% 0.78/1.41 Y := skol3
% 0.78/1.41 end
% 0.78/1.41 substitution1:
% 0.78/1.41 X := X
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 subsumption: (2982) {G9,W5,D3,L1,V1,M1} R(2968,72) { convergent_lines(
% 0.78/1.41 orthogonal_through_point( X, skol2 ), skol3 ) }.
% 0.78/1.41 parent0: (3862) {G2,W5,D3,L1,V1,M1} { convergent_lines(
% 0.78/1.41 orthogonal_through_point( X, skol2 ), skol3 ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := X
% 0.78/1.41 end
% 0.78/1.41 permutation0:
% 0.78/1.41 0 ==> 0
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 resolution: (3863) {G1,W13,D3,L3,V3,M3} { ! convergent_lines( Z,
% 0.78/1.41 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ), !
% 0.78/1.41 unorthogonal_lines( Z, orthogonal_through_point( X, Y ) ) }.
% 0.78/1.41 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 0.78/1.41 orthogonal_through_point( Y, X ), Y ) }.
% 0.78/1.41 parent1[3]: (171) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y
% 0.78/1.41 ), convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 0.78/1.41 unorthogonal_lines( Y, Z ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := Y
% 0.78/1.41 Y := X
% 0.78/1.41 end
% 0.78/1.41 substitution1:
% 0.78/1.41 X := Z
% 0.78/1.41 Y := orthogonal_through_point( X, Y )
% 0.78/1.41 Z := X
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 resolution: (3864) {G2,W11,D3,L3,V3,M3} { convergent_lines( X, Y ), !
% 0.78/1.41 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ),
% 0.78/1.41 convergent_lines( X, Y ) }.
% 0.78/1.41 parent0[0]: (3863) {G1,W13,D3,L3,V3,M3} { ! convergent_lines( Z,
% 0.78/1.41 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ), !
% 0.78/1.41 unorthogonal_lines( Z, orthogonal_through_point( X, Y ) ) }.
% 0.78/1.41 parent1[0]: (192) {G4,W8,D3,L2,V3,M2} R(177,72) { convergent_lines( X,
% 0.78/1.41 orthogonal_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := Y
% 0.78/1.41 Y := Z
% 0.78/1.41 Z := X
% 0.78/1.41 end
% 0.78/1.41 substitution1:
% 0.78/1.41 X := X
% 0.78/1.41 Y := Y
% 0.78/1.41 Z := Z
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 factor: (3865) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 0.78/1.41 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 0.78/1.41 parent0[0, 2]: (3864) {G2,W11,D3,L3,V3,M3} { convergent_lines( X, Y ), !
% 0.78/1.41 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ),
% 0.78/1.41 convergent_lines( X, Y ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := X
% 0.78/1.41 Y := Y
% 0.78/1.41 Z := Z
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 subsumption: (3469) {G5,W8,D3,L2,V3,M1} R(171,23);r(192) { convergent_lines
% 0.78/1.41 ( X, Y ), ! unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 0.78/1.41 parent0: (3865) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 0.78/1.41 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := X
% 0.78/1.41 Y := Y
% 0.78/1.41 Z := Z
% 0.78/1.41 end
% 0.78/1.41 permutation0:
% 0.78/1.41 0 ==> 0
% 0.78/1.41 1 ==> 1
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 resolution: (3866) {G2,W10,D3,L2,V4,M2} { convergent_lines(
% 0.78/1.41 orthogonal_through_point( X, Y ), Z ), ! convergent_lines(
% 0.78/1.41 orthogonal_through_point( Z, T ), X ) }.
% 0.78/1.41 parent0[1]: (3469) {G5,W8,D3,L2,V3,M1} R(171,23);r(192) { convergent_lines
% 0.78/1.41 ( X, Y ), ! unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 0.78/1.41 parent1[1]: (280) {G1,W8,D3,L2,V3,M1} R(31,23) { ! convergent_lines( X, Y )
% 0.78/1.41 , unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := orthogonal_through_point( X, Y )
% 0.78/1.41 Y := Z
% 0.78/1.41 Z := T
% 0.78/1.41 end
% 0.78/1.41 substitution1:
% 0.78/1.41 X := orthogonal_through_point( Z, T )
% 0.78/1.41 Y := X
% 0.78/1.41 Z := Y
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 subsumption: (3476) {G6,W10,D3,L2,V4,M2} R(3469,280) { ! convergent_lines(
% 0.78/1.41 orthogonal_through_point( Z, T ), X ), convergent_lines(
% 0.78/1.41 orthogonal_through_point( X, Y ), Z ) }.
% 0.78/1.41 parent0: (3866) {G2,W10,D3,L2,V4,M2} { convergent_lines(
% 0.78/1.41 orthogonal_through_point( X, Y ), Z ), ! convergent_lines(
% 0.78/1.41 orthogonal_through_point( Z, T ), X ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := X
% 0.78/1.41 Y := Y
% 0.78/1.41 Z := Z
% 0.78/1.41 T := T
% 0.78/1.41 end
% 0.78/1.41 permutation0:
% 0.78/1.41 0 ==> 1
% 0.78/1.41 1 ==> 0
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 resolution: (3867) {G7,W5,D3,L1,V2,M1} { convergent_lines(
% 0.78/1.41 orthogonal_through_point( skol3, Y ), X ) }.
% 0.78/1.41 parent0[0]: (3476) {G6,W10,D3,L2,V4,M2} R(3469,280) { ! convergent_lines(
% 0.78/1.41 orthogonal_through_point( Z, T ), X ), convergent_lines(
% 0.78/1.41 orthogonal_through_point( X, Y ), Z ) }.
% 0.78/1.41 parent1[0]: (2982) {G9,W5,D3,L1,V1,M1} R(2968,72) { convergent_lines(
% 0.78/1.41 orthogonal_through_point( X, skol2 ), skol3 ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := skol3
% 0.78/1.41 Y := Y
% 0.78/1.41 Z := X
% 0.78/1.41 T := skol2
% 0.78/1.41 end
% 0.78/1.41 substitution1:
% 0.78/1.41 X := X
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 subsumption: (3500) {G10,W5,D3,L1,V2,M1} R(3476,2982) { convergent_lines(
% 0.78/1.41 orthogonal_through_point( skol3, X ), Y ) }.
% 0.78/1.41 parent0: (3867) {G7,W5,D3,L1,V2,M1} { convergent_lines(
% 0.78/1.41 orthogonal_through_point( skol3, Y ), X ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := Y
% 0.78/1.41 Y := X
% 0.78/1.41 end
% 0.78/1.41 permutation0:
% 0.78/1.41 0 ==> 0
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 resolution: (3868) {G7,W0,D0,L0,V0,M0} { }.
% 0.78/1.41 parent0[0]: (240) {G6,W9,D5,L1,V4,M1} R(236,77) { ! convergent_lines( X,
% 0.78/1.41 parallel_through_point( parallel_through_point( parallel_through_point( X
% 0.78/1.41 , Y ), Z ), T ) ) }.
% 0.78/1.41 parent1[0]: (3500) {G10,W5,D3,L1,V2,M1} R(3476,2982) { convergent_lines(
% 0.78/1.41 orthogonal_through_point( skol3, X ), Y ) }.
% 0.78/1.41 substitution0:
% 0.78/1.41 X := orthogonal_through_point( skol3, X )
% 0.78/1.41 Y := Y
% 0.78/1.41 Z := Z
% 0.78/1.41 T := T
% 0.78/1.41 end
% 0.78/1.41 substitution1:
% 0.78/1.41 X := X
% 0.78/1.41 Y := parallel_through_point( parallel_through_point(
% 0.78/1.41 parallel_through_point( orthogonal_through_point( skol3, X ), Y ), Z ), T
% 0.78/1.41 )
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 subsumption: (3585) {G11,W0,D0,L0,V0,M0} R(3500,240) { }.
% 0.78/1.41 parent0: (3868) {G7,W0,D0,L0,V0,M0} { }.
% 0.78/1.41 substitution0:
% 0.78/1.41 end
% 0.78/1.41 permutation0:
% 0.78/1.41 end
% 0.78/1.41
% 0.78/1.41 Proof check complete!
% 0.78/1.41
% 0.78/1.41 Memory use:
% 0.78/1.41
% 0.78/1.41 space for terms: 47533
% 0.78/1.41 space for clauses: 144604
% 0.78/1.41
% 0.78/1.41
% 0.78/1.41 clauses generated: 19856
% 0.78/1.41 clauses kept: 3586
% 0.78/1.41 clauses selected: 456
% 0.78/1.41 clauses deleted: 6
% 0.78/1.41 clauses inuse deleted: 2
% 0.78/1.41
% 0.78/1.41 subsentry: 271977
% 0.78/1.41 literals s-matched: 110521
% 0.78/1.41 literals matched: 110441
% 0.78/1.41 full subsumption: 65366
% 0.78/1.41
% 0.78/1.41 checksum: 2136189037
% 0.78/1.41
% 0.78/1.41
% 0.78/1.41 Bliksem ended
%------------------------------------------------------------------------------