TSTP Solution File: GEO176+3 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO176+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n022.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 02:52:17 EDT 2022
% Result : Theorem 0.72s 1.23s
% Output : Refutation 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO176+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Fri Jun 17 22:38:32 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.72/1.23 *** allocated 10000 integers for termspace/termends
% 0.72/1.23 *** allocated 10000 integers for clauses
% 0.72/1.23 *** allocated 10000 integers for justifications
% 0.72/1.23 Bliksem 1.12
% 0.72/1.23
% 0.72/1.23
% 0.72/1.23 Automatic Strategy Selection
% 0.72/1.23
% 0.72/1.23
% 0.72/1.23 Clauses:
% 0.72/1.23
% 0.72/1.23 { ! distinct_points( X, X ) }.
% 0.72/1.23 { ! distinct_lines( X, X ) }.
% 0.72/1.23 { ! convergent_lines( X, X ) }.
% 0.72/1.23 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 0.72/1.23 ) }.
% 0.72/1.23 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.72/1.23 }.
% 0.72/1.23 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 0.72/1.23 , Z ) }.
% 0.72/1.23 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 0.72/1.23 , Y ) ) }.
% 0.72/1.23 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 0.72/1.23 , Y ) ) }.
% 0.72/1.23 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.72/1.23 , Y ), X ) }.
% 0.72/1.23 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.72/1.23 , Y ), Y ) }.
% 0.72/1.23 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 0.72/1.23 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 0.72/1.23 apart_point_and_line( Y, T ) }.
% 0.72/1.23 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 0.72/1.23 apart_point_and_line( Z, Y ) }.
% 0.72/1.23 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 0.72/1.23 apart_point_and_line( X, Z ) }.
% 0.72/1.23 { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X,
% 0.72/1.23 Z ) }.
% 0.72/1.23 { ! distinct_lines( X, Y ), convergent_lines( X, Y ) }.
% 0.72/1.23 { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 0.72/1.23 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 0.72/1.23 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 0.72/1.23 apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 0.72/1.23 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.72/1.23 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.72/1.23 , convergent_lines( Y, Z ) }.
% 0.72/1.23 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.72/1.23 , unorthogonal_lines( Y, Z ) }.
% 0.72/1.23 { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 0.72/1.23 { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.72/1.23 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 0.72/1.23 }.
% 0.72/1.23 { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 0.72/1.23 { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 0.72/1.23 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 0.72/1.23 apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ),
% 0.72/1.23 unorthogonal_lines( Y, T ) }.
% 0.72/1.23 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.72/1.23 { alpha2( X, Z ), convergent_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 0.72/1.23 unorthogonal_lines( X, Y ) }.
% 0.72/1.23 { alpha2( X, Z ), unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 0.72/1.23 unorthogonal_lines( X, Y ) }.
% 0.72/1.23 { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 0.72/1.23 { ! alpha2( X, Y ), unorthogonal_lines( Y, X ) }.
% 0.72/1.23 { ! convergent_lines( Y, X ), ! unorthogonal_lines( Y, X ), alpha2( X, Y )
% 0.72/1.23 }.
% 0.72/1.23 { unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ), !
% 0.72/1.23 convergent_lines( X, Y ) }.
% 0.72/1.23 { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line(
% 0.72/1.23 line_connecting( X, Y ) ) }.
% 0.72/1.23 { ! line( X ), ! line( Y ), ! convergent_lines( X, Y ), point(
% 0.72/1.23 intersection_point( X, Y ) ) }.
% 0.72/1.23 { ! line( X ), ! point( Y ), line( parallel_through_point( X, Y ) ) }.
% 0.72/1.23 { ! line( X ), ! point( Y ), line( orthogonal_through_point( X, Y ) ) }.
% 0.72/1.23 { ! equal_points( X, Y ), ! distinct_points( X, Y ) }.
% 0.72/1.23 { distinct_points( X, Y ), equal_points( X, Y ) }.
% 0.72/1.23 { ! equal_lines( X, Y ), ! distinct_lines( X, Y ) }.
% 0.72/1.23 { distinct_lines( X, Y ), equal_lines( X, Y ) }.
% 0.72/1.23 { ! parallel_lines( X, Y ), ! convergent_lines( X, Y ) }.
% 0.72/1.23 { convergent_lines( X, Y ), parallel_lines( X, Y ) }.
% 0.72/1.23 { ! incident_point_and_line( X, Y ), ! apart_point_and_line( X, Y ) }.
% 0.72/1.23 { apart_point_and_line( X, Y ), incident_point_and_line( X, Y ) }.
% 0.72/1.23 { ! orthogonal_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.72/1.23 { unorthogonal_lines( X, Y ), orthogonal_lines( X, Y ) }.
% 0.72/1.23 { distinct_points( skol1, skol4 ) }.
% 0.72/1.23 { convergent_lines( skol2, skol3 ) }.
% 0.72/1.23 { apart_point_and_line( skol1, skol2 ), apart_point_and_line( skol1, skol3
% 0.72/1.23 ) }.
% 0.72/1.23 { ! distinct_points( skol1, intersection_point( skol2, skol3 ) ) }.
% 0.72/1.23
% 0.72/1.23 percentage equality = 0.000000, percentage horn = 0.600000
% 0.72/1.23 This a non-horn, non-equality problem
% 0.72/1.23
% 0.72/1.23
% 0.72/1.23 Options Used:
% 0.72/1.23
% 0.72/1.23 useres = 1
% 0.72/1.23 useparamod = 0
% 0.72/1.23 useeqrefl = 0
% 0.72/1.23 useeqfact = 0
% 0.72/1.23 usefactor = 1
% 0.72/1.23 usesimpsplitting = 0
% 0.72/1.23 usesimpdemod = 0
% 0.72/1.23 usesimpres = 3
% 0.72/1.23
% 0.72/1.23 resimpinuse = 1000
% 0.72/1.23 resimpclauses = 20000
% 0.72/1.23 substype = standard
% 0.72/1.23 backwardsubs = 1
% 0.72/1.23 selectoldest = 5
% 0.72/1.23
% 0.72/1.23 litorderings [0] = split
% 0.72/1.23 litorderings [1] = liftord
% 0.72/1.23
% 0.72/1.23 termordering = none
% 0.72/1.23
% 0.72/1.23 litapriori = 1
% 0.72/1.23 termapriori = 0
% 0.72/1.23 litaposteriori = 0
% 0.72/1.23 termaposteriori = 0
% 0.72/1.23 demodaposteriori = 0
% 0.72/1.23 ordereqreflfact = 0
% 0.72/1.23
% 0.72/1.23 litselect = none
% 0.72/1.23
% 0.72/1.23 maxweight = 15
% 0.72/1.23 maxdepth = 30000
% 0.72/1.23 maxlength = 115
% 0.72/1.23 maxnrvars = 195
% 0.72/1.23 excuselevel = 1
% 0.72/1.23 increasemaxweight = 1
% 0.72/1.23
% 0.72/1.23 maxselected = 10000000
% 0.72/1.23 maxnrclauses = 10000000
% 0.72/1.23
% 0.72/1.23 showgenerated = 0
% 0.72/1.23 showkept = 0
% 0.72/1.23 showselected = 0
% 0.72/1.23 showdeleted = 0
% 0.72/1.23 showresimp = 1
% 0.72/1.23 showstatus = 2000
% 0.72/1.23
% 0.72/1.23 prologoutput = 0
% 0.72/1.23 nrgoals = 5000000
% 0.72/1.23 totalproof = 1
% 0.72/1.23
% 0.72/1.23 Symbols occurring in the translation:
% 0.72/1.23
% 0.72/1.23 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.72/1.23 . [1, 2] (w:1, o:27, a:1, s:1, b:0),
% 0.72/1.23 ! [4, 1] (w:0, o:20, a:1, s:1, b:0),
% 0.72/1.23 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.72/1.23 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.72/1.23 distinct_points [36, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.72/1.23 distinct_lines [37, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.72/1.23 convergent_lines [38, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.72/1.23 line_connecting [41, 2] (w:1, o:54, a:1, s:1, b:0),
% 0.72/1.23 apart_point_and_line [42, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.72/1.23 intersection_point [43, 2] (w:1, o:56, a:1, s:1, b:0),
% 0.72/1.23 parallel_through_point [46, 2] (w:1, o:59, a:1, s:1, b:0),
% 0.72/1.23 unorthogonal_lines [49, 2] (w:1, o:60, a:1, s:1, b:0),
% 0.72/1.23 orthogonal_through_point [52, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.72/1.23 point [54, 1] (w:1, o:25, a:1, s:1, b:0),
% 0.72/1.23 line [55, 1] (w:1, o:26, a:1, s:1, b:0),
% 0.72/1.23 equal_points [56, 2] (w:1, o:61, a:1, s:1, b:0),
% 0.72/1.23 equal_lines [57, 2] (w:1, o:62, a:1, s:1, b:0),
% 0.72/1.23 parallel_lines [58, 2] (w:1, o:63, a:1, s:1, b:0),
% 0.72/1.23 incident_point_and_line [59, 2] (w:1, o:64, a:1, s:1, b:0),
% 0.72/1.23 orthogonal_lines [60, 2] (w:1, o:58, a:1, s:1, b:0),
% 0.72/1.23 alpha1 [61, 2] (w:1, o:65, a:1, s:1, b:0),
% 0.72/1.23 alpha2 [62, 2] (w:1, o:66, a:1, s:1, b:0),
% 0.72/1.23 skol1 [63, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.72/1.23 skol2 [64, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.72/1.23 skol3 [65, 0] (w:1, o:18, a:1, s:1, b:0),
% 0.72/1.23 skol4 [66, 0] (w:1, o:19, a:1, s:1, b:0).
% 0.72/1.23
% 0.72/1.23
% 0.72/1.23 Starting Search:
% 0.72/1.23
% 0.72/1.23 *** allocated 15000 integers for clauses
% 0.72/1.23 *** allocated 22500 integers for clauses
% 0.72/1.23 *** allocated 33750 integers for clauses
% 0.72/1.23 *** allocated 15000 integers for termspace/termends
% 0.72/1.23 *** allocated 50625 integers for clauses
% 0.72/1.23 Resimplifying inuse:
% 0.72/1.23 Done
% 0.72/1.23
% 0.72/1.23 *** allocated 22500 integers for termspace/termends
% 0.72/1.23 *** allocated 75937 integers for clauses
% 0.72/1.23 *** allocated 33750 integers for termspace/termends
% 0.72/1.23 *** allocated 113905 integers for clauses
% 0.72/1.23
% 0.72/1.23 Intermediate Status:
% 0.72/1.23 Generated: 10086
% 0.72/1.23 Kept: 2006
% 0.72/1.23 Inuse: 316
% 0.72/1.23 Deleted: 1
% 0.72/1.23 Deletedinuse: 0
% 0.72/1.23
% 0.72/1.23 Resimplifying inuse:
% 0.72/1.23 Done
% 0.72/1.23
% 0.72/1.23 *** allocated 50625 integers for termspace/termends
% 0.72/1.23 *** allocated 170857 integers for clauses
% 0.72/1.23 Resimplifying inuse:
% 0.72/1.23 Done
% 0.72/1.23
% 0.72/1.23
% 0.72/1.23 Bliksems!, er is een bewijs:
% 0.72/1.23 % SZS status Theorem
% 0.72/1.23 % SZS output start Refutation
% 0.72/1.23
% 0.72/1.23 (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.72/1.23 (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.72/1.23 (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.72/1.23 , ! distinct_lines( X, Y ) }.
% 0.72/1.23 (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), convergent_lines( Y,
% 0.72/1.23 Z ), ! convergent_lines( X, Y ) }.
% 0.72/1.23 (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), apart_point_and_line(
% 0.72/1.23 X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.72/1.23 (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! distinct_lines( X
% 0.72/1.23 , Y ) }.
% 0.72/1.23 (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines( parallel_through_point( Y
% 0.72/1.23 , X ), Y ) }.
% 0.72/1.23 (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.72/1.23 parallel_through_point( Y, X ) ) }.
% 0.72/1.23 (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), unorthogonal_lines(
% 0.72/1.23 X, Y ) }.
% 0.72/1.23 (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 0.72/1.23 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 0.72/1.23 }.
% 0.72/1.23 (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! alpha1( X, Y ) }.
% 0.72/1.23 (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( orthogonal_through_point
% 0.72/1.23 ( Y, X ), Y ) }.
% 0.72/1.23 (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.72/1.23 orthogonal_through_point( Y, X ) ) }.
% 0.72/1.23 (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ), unorthogonal_lines
% 0.72/1.23 ( Z, X ), unorthogonal_lines( Z, Y ) }.
% 0.72/1.23 (48) {G0,W6,D2,L2,V0,M1} I { apart_point_and_line( skol1, skol2 ),
% 0.72/1.23 apart_point_and_line( skol1, skol3 ) }.
% 0.72/1.23 (56) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 0.72/1.23 ( X, Y ) }.
% 0.72/1.23 (70) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.72/1.23 convergent_lines( X, Y ) }.
% 0.72/1.23 (75) {G2,W5,D3,L1,V2,M1} R(70,15) { ! convergent_lines( X,
% 0.72/1.23 parallel_through_point( X, Y ) ) }.
% 0.72/1.23 (77) {G3,W8,D3,L2,V3,M2} R(75,5) { ! convergent_lines( Y, X ),
% 0.72/1.23 convergent_lines( X, parallel_through_point( Y, Z ) ) }.
% 0.72/1.23 (81) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 0.72/1.23 orthogonal_through_point( X, Y ), X ) }.
% 0.72/1.23 (109) {G2,W8,D3,L2,V3,M2} R(81,5) { convergent_lines( X, Z ),
% 0.72/1.23 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.72/1.23 (110) {G2,W6,D2,L2,V2,M1} R(14,56) { convergent_lines( X, Y ), !
% 0.72/1.23 distinct_lines( Y, X ) }.
% 0.72/1.23 (131) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ),
% 0.72/1.23 distinct_lines( Y, T ), apart_point_and_line( Z, T ), !
% 0.72/1.23 apart_point_and_line( Z, X ) }.
% 0.72/1.23 (141) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X,
% 0.72/1.23 parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.23 (142) {G1,W8,D3,L2,V3,M1} R(12,24) { distinct_lines( X,
% 0.72/1.23 orthogonal_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.23 (167) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y ),
% 0.72/1.23 convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 0.72/1.23 unorthogonal_lines( Y, Z ) }.
% 0.72/1.23 (183) {G3,W8,D3,L2,V3,M2} R(109,70) { convergent_lines( Z, X ),
% 0.72/1.23 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.72/1.23 (200) {G4,W8,D3,L2,V3,M2} R(183,70) { convergent_lines( X,
% 0.72/1.23 orthogonal_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 0.72/1.23 (232) {G4,W7,D4,L1,V3,M1} R(77,15) { ! convergent_lines( X,
% 0.72/1.23 parallel_through_point( parallel_through_point( X, Y ), Z ) ) }.
% 0.72/1.23 (243) {G5,W7,D4,L1,V3,M1} R(232,70) { ! convergent_lines(
% 0.72/1.23 parallel_through_point( parallel_through_point( X, Y ), Z ), X ) }.
% 0.72/1.23 (246) {G6,W9,D5,L1,V4,M1} R(243,77) { ! convergent_lines( X,
% 0.72/1.23 parallel_through_point( parallel_through_point( parallel_through_point( X
% 0.72/1.23 , Y ), Z ), T ) ) }.
% 0.72/1.23 (258) {G1,W8,D3,L2,V3,M1} R(31,23) { ! convergent_lines( X, Y ),
% 0.72/1.23 unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 0.72/1.23 (2390) {G2,W14,D3,L4,V5,M1} R(131,142) { distinct_lines( X, Y ),
% 0.72/1.23 distinct_lines( Y, Z ), distinct_lines( Z, orthogonal_through_point( U, T
% 0.72/1.23 ) ), ! apart_point_and_line( T, X ) }.
% 0.72/1.23 (2391) {G2,W14,D3,L4,V5,M1} R(131,141) { distinct_lines( X, Y ),
% 0.72/1.23 distinct_lines( Y, Z ), distinct_lines( Z, parallel_through_point( U, T )
% 0.72/1.23 ), ! apart_point_and_line( T, X ) }.
% 0.72/1.23 (2399) {G3,W8,D3,L2,V3,M1} F(2391);r(56) { distinct_lines(
% 0.72/1.23 parallel_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.23 (2400) {G3,W8,D3,L2,V3,M1} F(2390);r(56) { distinct_lines(
% 0.72/1.23 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.23 (2421) {G4,W8,D3,L2,V1,M1} R(2400,48) { distinct_lines(
% 0.72/1.23 orthogonal_through_point( X, skol1 ), skol3 ), apart_point_and_line(
% 0.72/1.23 skol1, skol2 ) }.
% 0.72/1.23 (2456) {G5,W10,D3,L2,V2,M1} R(2421,2399) { distinct_lines(
% 0.72/1.23 parallel_through_point( Y, skol1 ), skol2 ), distinct_lines(
% 0.72/1.23 orthogonal_through_point( X, skol1 ), skol3 ) }.
% 0.72/1.23 (2793) {G6,W10,D3,L2,V2,M1} R(2456,110) { convergent_lines( skol3,
% 0.72/1.23 orthogonal_through_point( Y, skol1 ) ), distinct_lines(
% 0.72/1.23 parallel_through_point( X, skol1 ), skol2 ) }.
% 0.72/1.23 (2811) {G7,W10,D3,L2,V2,M1} R(2793,110) { convergent_lines( skol3,
% 0.72/1.23 orthogonal_through_point( X, skol1 ) ), convergent_lines( skol2,
% 0.72/1.23 parallel_through_point( Y, skol1 ) ) }.
% 0.72/1.23 (2821) {G8,W5,D3,L1,V1,M1} R(2811,246) { convergent_lines( skol3,
% 0.72/1.23 orthogonal_through_point( X, skol1 ) ) }.
% 0.72/1.23 (2834) {G9,W5,D3,L1,V1,M1} R(2821,70) { convergent_lines(
% 0.72/1.23 orthogonal_through_point( X, skol1 ), skol3 ) }.
% 0.72/1.23 (3103) {G5,W8,D3,L2,V3,M1} R(167,23);r(200) { convergent_lines( X, Y ), !
% 0.72/1.23 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 0.72/1.23 (3110) {G6,W10,D3,L2,V4,M2} R(3103,258) { ! convergent_lines(
% 0.72/1.23 orthogonal_through_point( Z, T ), X ), convergent_lines(
% 0.72/1.23 orthogonal_through_point( X, Y ), Z ) }.
% 0.72/1.23 (3125) {G10,W5,D3,L1,V2,M1} R(3110,2834) { convergent_lines(
% 0.72/1.23 orthogonal_through_point( skol3, X ), Y ) }.
% 0.72/1.23 (3208) {G11,W0,D0,L0,V0,M0} R(3125,246) { }.
% 0.72/1.23
% 0.72/1.23
% 0.72/1.23 % SZS output end Refutation
% 0.72/1.23 found a proof!
% 0.72/1.23
% 0.72/1.23
% 0.72/1.23 Unprocessed initial clauses:
% 0.72/1.23
% 0.72/1.23 (3210) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 0.72/1.23 (3211) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.72/1.23 (3212) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 0.72/1.23 (3213) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 0.72/1.23 , Z ), distinct_points( Y, Z ) }.
% 0.72/1.23 (3214) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X,
% 0.72/1.23 Z ), distinct_lines( Y, Z ) }.
% 0.72/1.23 (3215) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines
% 0.72/1.23 ( X, Z ), convergent_lines( Y, Z ) }.
% 0.72/1.23 (3216) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.72/1.23 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 0.72/1.23 (3217) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.72/1.23 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 0.72/1.23 (3218) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 0.72/1.23 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 0.72/1.23 (3219) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 0.72/1.23 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 0.72/1.23 (3220) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines
% 0.72/1.23 ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 0.72/1.23 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 0.72/1.23 (3221) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 0.72/1.23 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 0.72/1.23 (3222) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 0.72/1.23 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 0.72/1.23 (3223) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), distinct_lines( Y
% 0.72/1.23 , Z ), convergent_lines( X, Z ) }.
% 0.72/1.23 (3224) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ), convergent_lines( X
% 0.72/1.23 , Y ) }.
% 0.72/1.23 (3225) {G0,W5,D3,L1,V2,M1} { ! convergent_lines( parallel_through_point( Y
% 0.72/1.23 , X ), Y ) }.
% 0.72/1.23 (3226) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.72/1.23 parallel_through_point( Y, X ) ) }.
% 0.72/1.23 (3227) {G0,W12,D2,L4,V3,M4} { ! distinct_lines( X, Y ),
% 0.72/1.23 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 0.72/1.23 convergent_lines( X, Y ) }.
% 0.72/1.23 (3228) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines
% 0.72/1.23 ( X, Y ) }.
% 0.72/1.23 (3229) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.72/1.23 unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 0.72/1.23 (3230) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.72/1.23 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 0.72/1.23 }.
% 0.72/1.23 (3231) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines( X, Y )
% 0.72/1.23 }.
% 0.72/1.23 (3232) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 0.72/1.23 }.
% 0.72/1.23 (3233) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( X, Y ), !
% 0.72/1.23 unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 0.72/1.23 (3234) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines(
% 0.72/1.23 orthogonal_through_point( Y, X ), Y ) }.
% 0.72/1.23 (3235) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.72/1.23 orthogonal_through_point( Y, X ) ) }.
% 0.72/1.23 (3236) {G0,W15,D2,L5,V4,M5} { ! distinct_lines( X, Y ),
% 0.72/1.23 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 0.72/1.23 unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 0.72/1.23 (3237) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines
% 0.72/1.23 ( X, Y ) }.
% 0.72/1.23 (3238) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), convergent_lines( Z, Y ), !
% 0.72/1.23 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.72/1.23 (3239) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), unorthogonal_lines( Z, Y ),
% 0.72/1.23 ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.72/1.23 (3240) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), convergent_lines( Y, X )
% 0.72/1.23 }.
% 0.72/1.23 (3241) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), unorthogonal_lines( Y, X )
% 0.72/1.23 }.
% 0.72/1.23 (3242) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( Y, X ), !
% 0.72/1.23 unorthogonal_lines( Y, X ), alpha2( X, Y ) }.
% 0.72/1.23 (3243) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ),
% 0.72/1.23 unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 0.72/1.23 (3244) {G0,W11,D3,L4,V2,M4} { ! point( X ), ! point( Y ), !
% 0.72/1.23 distinct_points( X, Y ), line( line_connecting( X, Y ) ) }.
% 0.72/1.23 (3245) {G0,W11,D3,L4,V2,M4} { ! line( X ), ! line( Y ), ! convergent_lines
% 0.72/1.23 ( X, Y ), point( intersection_point( X, Y ) ) }.
% 0.72/1.23 (3246) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 0.72/1.23 parallel_through_point( X, Y ) ) }.
% 0.72/1.23 (3247) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 0.72/1.23 orthogonal_through_point( X, Y ) ) }.
% 0.72/1.23 (3248) {G0,W6,D2,L2,V2,M2} { ! equal_points( X, Y ), ! distinct_points( X
% 0.72/1.23 , Y ) }.
% 0.72/1.23 (3249) {G0,W6,D2,L2,V2,M2} { distinct_points( X, Y ), equal_points( X, Y )
% 0.72/1.23 }.
% 0.72/1.23 (3250) {G0,W6,D2,L2,V2,M2} { ! equal_lines( X, Y ), ! distinct_lines( X, Y
% 0.72/1.23 ) }.
% 0.72/1.23 (3251) {G0,W6,D2,L2,V2,M2} { distinct_lines( X, Y ), equal_lines( X, Y )
% 0.72/1.23 }.
% 0.72/1.23 (3252) {G0,W6,D2,L2,V2,M2} { ! parallel_lines( X, Y ), ! convergent_lines
% 0.72/1.23 ( X, Y ) }.
% 0.72/1.23 (3253) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), parallel_lines( X,
% 0.72/1.23 Y ) }.
% 0.72/1.23 (3254) {G0,W6,D2,L2,V2,M2} { ! incident_point_and_line( X, Y ), !
% 0.72/1.23 apart_point_and_line( X, Y ) }.
% 0.72/1.23 (3255) {G0,W6,D2,L2,V2,M2} { apart_point_and_line( X, Y ),
% 0.72/1.23 incident_point_and_line( X, Y ) }.
% 0.72/1.23 (3256) {G0,W6,D2,L2,V2,M2} { ! orthogonal_lines( X, Y ), !
% 0.72/1.23 unorthogonal_lines( X, Y ) }.
% 0.72/1.23 (3257) {G0,W6,D2,L2,V2,M2} { unorthogonal_lines( X, Y ), orthogonal_lines
% 0.72/1.23 ( X, Y ) }.
% 0.72/1.23 (3258) {G0,W3,D2,L1,V0,M1} { distinct_points( skol1, skol4 ) }.
% 0.72/1.23 (3259) {G0,W3,D2,L1,V0,M1} { convergent_lines( skol2, skol3 ) }.
% 0.72/1.23 (3260) {G0,W6,D2,L2,V0,M2} { apart_point_and_line( skol1, skol2 ),
% 0.72/1.23 apart_point_and_line( skol1, skol3 ) }.
% 0.72/1.23 (3261) {G0,W5,D3,L1,V0,M1} { ! distinct_points( skol1, intersection_point
% 0.72/1.23 ( skol2, skol3 ) ) }.
% 0.72/1.23
% 0.72/1.23
% 0.72/1.23 Total Proof:
% 0.72/1.23
% 0.72/1.23 subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.72/1.23 parent0: (3211) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.72/1.23 parent0: (3212) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 0.72/1.23 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 0.72/1.23 parent0: (3214) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ),
% 0.72/1.23 distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 2
% 0.72/1.23 1 ==> 0
% 0.72/1.23 2 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 0.72/1.23 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.72/1.23 parent0: (3215) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 0.72/1.23 convergent_lines( X, Z ), convergent_lines( Y, Z ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 2
% 0.72/1.23 1 ==> 0
% 0.72/1.23 2 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 0.72/1.23 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.72/1.23 parent0: (3222) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 0.72/1.23 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 2
% 0.72/1.23 1 ==> 0
% 0.72/1.23 2 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 0.72/1.23 distinct_lines( X, Y ) }.
% 0.72/1.23 parent0: (3224) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ),
% 0.72/1.23 convergent_lines( X, Y ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 1
% 0.72/1.23 1 ==> 0
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 0.72/1.23 parallel_through_point( Y, X ), Y ) }.
% 0.72/1.23 parent0: (3225) {G0,W5,D3,L1,V2,M1} { ! convergent_lines(
% 0.72/1.23 parallel_through_point( Y, X ), Y ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.72/1.23 parallel_through_point( Y, X ) ) }.
% 0.72/1.23 parent0: (3226) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.72/1.23 parallel_through_point( Y, X ) ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 0.72/1.23 unorthogonal_lines( X, Y ) }.
% 0.72/1.23 parent0: (3228) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ),
% 0.72/1.23 unorthogonal_lines( X, Y ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 0.72/1.23 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 0.72/1.23 }.
% 0.72/1.23 parent0: (3230) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.72/1.23 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 0.72/1.23 }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 2 ==> 3
% 0.72/1.23 3 ==> 2
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 0.72/1.23 alpha1( X, Y ) }.
% 0.72/1.23 parent0: (3231) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines(
% 0.72/1.23 X, Y ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 1
% 0.72/1.23 1 ==> 0
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 0.72/1.23 orthogonal_through_point( Y, X ), Y ) }.
% 0.72/1.23 parent0: (3234) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines(
% 0.72/1.23 orthogonal_through_point( Y, X ), Y ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.72/1.23 orthogonal_through_point( Y, X ) ) }.
% 0.72/1.23 parent0: (3235) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.72/1.23 orthogonal_through_point( Y, X ) ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ),
% 0.72/1.23 unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ) }.
% 0.72/1.23 parent0: (3243) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ),
% 0.72/1.23 unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 1
% 0.72/1.23 1 ==> 2
% 0.72/1.23 2 ==> 0
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (48) {G0,W6,D2,L2,V0,M1} I { apart_point_and_line( skol1,
% 0.72/1.23 skol2 ), apart_point_and_line( skol1, skol3 ) }.
% 0.72/1.23 parent0: (3260) {G0,W6,D2,L2,V0,M2} { apart_point_and_line( skol1, skol2 )
% 0.72/1.23 , apart_point_and_line( skol1, skol3 ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (3381) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 0.72/1.23 distinct_lines( X, Y ) }.
% 0.72/1.23 parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.72/1.23 parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 0.72/1.23 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := X
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (56) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 0.72/1.23 distinct_lines( X, Y ) }.
% 0.72/1.23 parent0: (3381) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 0.72/1.23 distinct_lines( X, Y ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Y
% 0.72/1.23 Y := X
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 1
% 0.72/1.23 1 ==> 0
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (3383) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 0.72/1.23 convergent_lines( X, Y ) }.
% 0.72/1.23 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.72/1.23 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 0.72/1.23 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := X
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (70) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.72/1.23 convergent_lines( X, Y ) }.
% 0.72/1.23 parent0: (3383) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 0.72/1.23 convergent_lines( X, Y ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Y
% 0.72/1.23 Y := X
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 1
% 0.72/1.23 1 ==> 0
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (3385) {G1,W5,D3,L1,V2,M1} { ! convergent_lines( X,
% 0.72/1.23 parallel_through_point( X, Y ) ) }.
% 0.72/1.23 parent0[0]: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 0.72/1.23 parallel_through_point( Y, X ), Y ) }.
% 0.72/1.23 parent1[1]: (70) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.72/1.23 convergent_lines( X, Y ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Y
% 0.72/1.23 Y := X
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := parallel_through_point( X, Y )
% 0.72/1.23 Y := X
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (75) {G2,W5,D3,L1,V2,M1} R(70,15) { ! convergent_lines( X,
% 0.72/1.23 parallel_through_point( X, Y ) ) }.
% 0.72/1.23 parent0: (3385) {G1,W5,D3,L1,V2,M1} { ! convergent_lines( X,
% 0.72/1.23 parallel_through_point( X, Y ) ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (3386) {G1,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 0.72/1.23 parallel_through_point( X, Y ) ), ! convergent_lines( X, Z ) }.
% 0.72/1.23 parent0[0]: (75) {G2,W5,D3,L1,V2,M1} R(70,15) { ! convergent_lines( X,
% 0.72/1.23 parallel_through_point( X, Y ) ) }.
% 0.72/1.23 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 0.72/1.23 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Z
% 0.72/1.23 Z := parallel_through_point( X, Y )
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (77) {G3,W8,D3,L2,V3,M2} R(75,5) { ! convergent_lines( Y, X )
% 0.72/1.23 , convergent_lines( X, parallel_through_point( Y, Z ) ) }.
% 0.72/1.23 parent0: (3386) {G1,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 0.72/1.23 parallel_through_point( X, Y ) ), ! convergent_lines( X, Z ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Y
% 0.72/1.23 Y := Z
% 0.72/1.23 Z := X
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 1
% 0.72/1.23 1 ==> 0
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (3388) {G1,W5,D3,L1,V2,M1} { convergent_lines(
% 0.72/1.23 orthogonal_through_point( X, Y ), X ) }.
% 0.72/1.23 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 0.72/1.23 orthogonal_through_point( Y, X ), Y ) }.
% 0.72/1.23 parent1[1]: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 0.72/1.23 unorthogonal_lines( X, Y ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Y
% 0.72/1.23 Y := X
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := orthogonal_through_point( X, Y )
% 0.72/1.23 Y := X
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (81) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 0.72/1.23 orthogonal_through_point( X, Y ), X ) }.
% 0.72/1.23 parent0: (3388) {G1,W5,D3,L1,V2,M1} { convergent_lines(
% 0.72/1.23 orthogonal_through_point( X, Y ), X ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (3389) {G1,W8,D3,L2,V3,M2} { convergent_lines(
% 0.72/1.23 orthogonal_through_point( X, Y ), Z ), convergent_lines( X, Z ) }.
% 0.72/1.23 parent0[2]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 0.72/1.23 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.72/1.23 parent1[0]: (81) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 0.72/1.23 orthogonal_through_point( X, Y ), X ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := orthogonal_through_point( X, Y )
% 0.72/1.23 Y := X
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (109) {G2,W8,D3,L2,V3,M2} R(81,5) { convergent_lines( X, Z ),
% 0.72/1.23 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.72/1.23 parent0: (3389) {G1,W8,D3,L2,V3,M2} { convergent_lines(
% 0.72/1.23 orthogonal_through_point( X, Y ), Z ), convergent_lines( X, Z ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 1
% 0.72/1.23 1 ==> 0
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (3390) {G1,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), !
% 0.72/1.23 distinct_lines( Y, X ) }.
% 0.72/1.23 parent0[1]: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 0.72/1.23 distinct_lines( X, Y ) }.
% 0.72/1.23 parent1[1]: (56) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 0.72/1.23 distinct_lines( X, Y ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (110) {G2,W6,D2,L2,V2,M1} R(14,56) { convergent_lines( X, Y )
% 0.72/1.23 , ! distinct_lines( Y, X ) }.
% 0.72/1.23 parent0: (3390) {G1,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), !
% 0.72/1.23 distinct_lines( Y, X ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (3391) {G1,W12,D2,L4,V4,M4} { distinct_lines( X, Y ),
% 0.72/1.23 apart_point_and_line( Z, Y ), distinct_lines( T, X ), !
% 0.72/1.23 apart_point_and_line( Z, T ) }.
% 0.72/1.23 parent0[2]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 0.72/1.23 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.72/1.23 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 0.72/1.23 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Z
% 0.72/1.23 Y := X
% 0.72/1.23 Z := Y
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := Z
% 0.72/1.23 Y := T
% 0.72/1.23 Z := X
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (131) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ),
% 0.72/1.23 distinct_lines( Y, T ), apart_point_and_line( Z, T ), !
% 0.72/1.23 apart_point_and_line( Z, X ) }.
% 0.72/1.23 parent0: (3391) {G1,W12,D2,L4,V4,M4} { distinct_lines( X, Y ),
% 0.72/1.23 apart_point_and_line( Z, Y ), distinct_lines( T, X ), !
% 0.72/1.23 apart_point_and_line( Z, T ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Y
% 0.72/1.23 Y := T
% 0.72/1.23 Z := Z
% 0.72/1.23 T := X
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 1
% 0.72/1.23 1 ==> 2
% 0.72/1.23 2 ==> 0
% 0.72/1.23 3 ==> 3
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (3393) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 0.72/1.23 parallel_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 0.72/1.23 parent0[0]: (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.72/1.23 parallel_through_point( Y, X ) ) }.
% 0.72/1.23 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 0.72/1.23 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Z
% 0.72/1.23 Z := parallel_through_point( Y, X )
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (141) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X,
% 0.72/1.23 parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.23 parent0: (3393) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 0.72/1.23 parallel_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Z
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := X
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (3394) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 0.72/1.23 orthogonal_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 0.72/1.23 parent0[0]: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.72/1.23 orthogonal_through_point( Y, X ) ) }.
% 0.72/1.23 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 0.72/1.23 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Z
% 0.72/1.23 Z := orthogonal_through_point( Y, X )
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (142) {G1,W8,D3,L2,V3,M1} R(12,24) { distinct_lines( X,
% 0.72/1.23 orthogonal_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.23 parent0: (3394) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 0.72/1.23 orthogonal_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Z
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := X
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (3396) {G1,W12,D2,L4,V3,M4} { convergent_lines( X, Y ), !
% 0.72/1.23 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ),
% 0.72/1.23 unorthogonal_lines( Z, Y ) }.
% 0.72/1.23 parent0[1]: (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! alpha1
% 0.72/1.23 ( X, Y ) }.
% 0.72/1.23 parent1[3]: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 0.72/1.23 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 0.72/1.23 }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Z
% 0.72/1.23 Z := Y
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (167) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y
% 0.72/1.23 ), convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 0.72/1.23 unorthogonal_lines( Y, Z ) }.
% 0.72/1.23 parent0: (3396) {G1,W12,D2,L4,V3,M4} { convergent_lines( X, Y ), !
% 0.72/1.23 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ),
% 0.72/1.23 unorthogonal_lines( Z, Y ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Z
% 0.72/1.23 Z := Y
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 1
% 0.72/1.23 1 ==> 0
% 0.72/1.23 2 ==> 2
% 0.72/1.23 3 ==> 3
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (3397) {G2,W8,D3,L2,V3,M2} { convergent_lines( Y, X ),
% 0.72/1.23 convergent_lines( orthogonal_through_point( X, Z ), Y ) }.
% 0.72/1.23 parent0[0]: (70) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.72/1.23 convergent_lines( X, Y ) }.
% 0.72/1.23 parent1[0]: (109) {G2,W8,D3,L2,V3,M2} R(81,5) { convergent_lines( X, Z ),
% 0.72/1.23 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Y
% 0.72/1.23 Y := X
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Z
% 0.72/1.23 Z := Y
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (183) {G3,W8,D3,L2,V3,M2} R(109,70) { convergent_lines( Z, X )
% 0.72/1.23 , convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.72/1.23 parent0: (3397) {G2,W8,D3,L2,V3,M2} { convergent_lines( Y, X ),
% 0.72/1.23 convergent_lines( orthogonal_through_point( X, Z ), Y ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Z
% 0.72/1.23 Z := Y
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (3400) {G2,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 0.72/1.23 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ) }.
% 0.72/1.23 parent0[0]: (70) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.72/1.23 convergent_lines( X, Y ) }.
% 0.72/1.23 parent1[1]: (183) {G3,W8,D3,L2,V3,M2} R(109,70) { convergent_lines( Z, X )
% 0.72/1.23 , convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Z
% 0.72/1.23 Y := orthogonal_through_point( X, Y )
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (200) {G4,W8,D3,L2,V3,M2} R(183,70) { convergent_lines( X,
% 0.72/1.23 orthogonal_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 0.72/1.23 parent0: (3400) {G2,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 0.72/1.23 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Y
% 0.72/1.23 Y := Z
% 0.72/1.23 Z := X
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (3401) {G1,W7,D4,L1,V3,M1} { ! convergent_lines( X,
% 0.72/1.23 parallel_through_point( parallel_through_point( X, Y ), Z ) ) }.
% 0.72/1.23 parent0[0]: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 0.72/1.23 parallel_through_point( Y, X ), Y ) }.
% 0.72/1.23 parent1[1]: (77) {G3,W8,D3,L2,V3,M2} R(75,5) { ! convergent_lines( Y, X ),
% 0.72/1.23 convergent_lines( X, parallel_through_point( Y, Z ) ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Z
% 0.72/1.23 Y := parallel_through_point( X, Y )
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := parallel_through_point( parallel_through_point( X, Y ), Z )
% 0.72/1.23 Y := X
% 0.72/1.23 Z := Y
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (232) {G4,W7,D4,L1,V3,M1} R(77,15) { ! convergent_lines( X,
% 0.72/1.23 parallel_through_point( parallel_through_point( X, Y ), Z ) ) }.
% 0.72/1.23 parent0: (3401) {G1,W7,D4,L1,V3,M1} { ! convergent_lines( X,
% 0.72/1.23 parallel_through_point( parallel_through_point( X, Y ), Z ) ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (3402) {G2,W7,D4,L1,V3,M1} { ! convergent_lines(
% 0.72/1.23 parallel_through_point( parallel_through_point( X, Y ), Z ), X ) }.
% 0.72/1.23 parent0[0]: (232) {G4,W7,D4,L1,V3,M1} R(77,15) { ! convergent_lines( X,
% 0.72/1.23 parallel_through_point( parallel_through_point( X, Y ), Z ) ) }.
% 0.72/1.23 parent1[1]: (70) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.72/1.23 convergent_lines( X, Y ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := X
% 0.72/1.23 Y := parallel_through_point( parallel_through_point( X, Y ), Z )
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (243) {G5,W7,D4,L1,V3,M1} R(232,70) { ! convergent_lines(
% 0.72/1.23 parallel_through_point( parallel_through_point( X, Y ), Z ), X ) }.
% 0.72/1.23 parent0: (3402) {G2,W7,D4,L1,V3,M1} { ! convergent_lines(
% 0.72/1.23 parallel_through_point( parallel_through_point( X, Y ), Z ), X ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (3403) {G4,W9,D5,L1,V4,M1} { ! convergent_lines( X,
% 0.72/1.23 parallel_through_point( parallel_through_point( parallel_through_point( X
% 0.72/1.23 , Y ), Z ), T ) ) }.
% 0.72/1.23 parent0[0]: (243) {G5,W7,D4,L1,V3,M1} R(232,70) { ! convergent_lines(
% 0.72/1.23 parallel_through_point( parallel_through_point( X, Y ), Z ), X ) }.
% 0.72/1.23 parent1[1]: (77) {G3,W8,D3,L2,V3,M2} R(75,5) { ! convergent_lines( Y, X ),
% 0.72/1.23 convergent_lines( X, parallel_through_point( Y, Z ) ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := parallel_through_point( X, Y )
% 0.72/1.23 Y := Z
% 0.72/1.23 Z := T
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := parallel_through_point( parallel_through_point(
% 0.72/1.23 parallel_through_point( X, Y ), Z ), T )
% 0.72/1.23 Y := X
% 0.72/1.23 Z := Y
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (246) {G6,W9,D5,L1,V4,M1} R(243,77) { ! convergent_lines( X,
% 0.72/1.23 parallel_through_point( parallel_through_point( parallel_through_point( X
% 0.72/1.23 , Y ), Z ), T ) ) }.
% 0.72/1.23 parent0: (3403) {G4,W9,D5,L1,V4,M1} { ! convergent_lines( X,
% 0.72/1.23 parallel_through_point( parallel_through_point( parallel_through_point( X
% 0.72/1.23 , Y ), Z ), T ) ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 T := T
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (3405) {G1,W8,D3,L2,V3,M2} { ! convergent_lines( Z, X ),
% 0.72/1.23 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.72/1.23 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 0.72/1.23 orthogonal_through_point( Y, X ), Y ) }.
% 0.72/1.23 parent1[2]: (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ),
% 0.72/1.23 unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Y
% 0.72/1.23 Y := X
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := Z
% 0.72/1.23 Y := X
% 0.72/1.23 Z := orthogonal_through_point( X, Y )
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (258) {G1,W8,D3,L2,V3,M1} R(31,23) { ! convergent_lines( X, Y
% 0.72/1.23 ), unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 0.72/1.23 parent0: (3405) {G1,W8,D3,L2,V3,M2} { ! convergent_lines( Z, X ),
% 0.72/1.23 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Y
% 0.72/1.23 Y := Z
% 0.72/1.23 Z := X
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (3406) {G2,W14,D3,L4,V5,M4} { distinct_lines( X,
% 0.72/1.23 orthogonal_through_point( Y, Z ) ), distinct_lines( T, U ),
% 0.72/1.23 distinct_lines( U, X ), ! apart_point_and_line( Z, T ) }.
% 0.72/1.23 parent0[1]: (142) {G1,W8,D3,L2,V3,M1} R(12,24) { distinct_lines( X,
% 0.72/1.23 orthogonal_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.23 parent1[2]: (131) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ),
% 0.72/1.23 distinct_lines( Y, T ), apart_point_and_line( Z, T ), !
% 0.72/1.23 apart_point_and_line( Z, X ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := T
% 0.72/1.23 Y := U
% 0.72/1.23 Z := Z
% 0.72/1.23 T := X
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (2390) {G2,W14,D3,L4,V5,M1} R(131,142) { distinct_lines( X, Y
% 0.72/1.23 ), distinct_lines( Y, Z ), distinct_lines( Z, orthogonal_through_point(
% 0.72/1.23 U, T ) ), ! apart_point_and_line( T, X ) }.
% 0.72/1.23 parent0: (3406) {G2,W14,D3,L4,V5,M4} { distinct_lines( X,
% 0.72/1.23 orthogonal_through_point( Y, Z ) ), distinct_lines( T, U ),
% 0.72/1.23 distinct_lines( U, X ), ! apart_point_and_line( Z, T ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Z
% 0.72/1.23 Y := U
% 0.72/1.23 Z := T
% 0.72/1.23 T := X
% 0.72/1.23 U := Y
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 2
% 0.72/1.23 1 ==> 0
% 0.72/1.23 2 ==> 1
% 0.72/1.23 3 ==> 3
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (3411) {G2,W14,D3,L4,V5,M4} { distinct_lines( X,
% 0.72/1.23 parallel_through_point( Y, Z ) ), distinct_lines( T, U ), distinct_lines
% 0.72/1.23 ( U, X ), ! apart_point_and_line( Z, T ) }.
% 0.72/1.23 parent0[1]: (141) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X,
% 0.72/1.23 parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.23 parent1[2]: (131) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ),
% 0.72/1.23 distinct_lines( Y, T ), apart_point_and_line( Z, T ), !
% 0.72/1.23 apart_point_and_line( Z, X ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := T
% 0.72/1.23 Y := U
% 0.72/1.23 Z := Z
% 0.72/1.23 T := X
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (2391) {G2,W14,D3,L4,V5,M1} R(131,141) { distinct_lines( X, Y
% 0.72/1.23 ), distinct_lines( Y, Z ), distinct_lines( Z, parallel_through_point( U
% 0.72/1.23 , T ) ), ! apart_point_and_line( T, X ) }.
% 0.72/1.23 parent0: (3411) {G2,W14,D3,L4,V5,M4} { distinct_lines( X,
% 0.72/1.23 parallel_through_point( Y, Z ) ), distinct_lines( T, U ), distinct_lines
% 0.72/1.23 ( U, X ), ! apart_point_and_line( Z, T ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Z
% 0.72/1.23 Y := U
% 0.72/1.23 Z := T
% 0.72/1.23 T := X
% 0.72/1.23 U := Y
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 2
% 0.72/1.23 1 ==> 0
% 0.72/1.23 2 ==> 1
% 0.72/1.23 3 ==> 3
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 factor: (3417) {G2,W13,D3,L3,V3,M3} { distinct_lines( X,
% 0.72/1.23 parallel_through_point( Y, Z ) ), distinct_lines( parallel_through_point
% 0.72/1.23 ( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.23 parent0[0, 2]: (2391) {G2,W14,D3,L4,V5,M1} R(131,141) { distinct_lines( X,
% 0.72/1.23 Y ), distinct_lines( Y, Z ), distinct_lines( Z, parallel_through_point( U
% 0.72/1.23 , T ) ), ! apart_point_and_line( T, X ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := parallel_through_point( Y, Z )
% 0.72/1.23 Z := X
% 0.72/1.23 T := Z
% 0.72/1.23 U := Y
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (3423) {G2,W13,D3,L3,V3,M3} { distinct_lines(
% 0.72/1.23 parallel_through_point( Y, Z ), X ), distinct_lines(
% 0.72/1.23 parallel_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.23 parent0[0]: (56) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 0.72/1.23 distinct_lines( X, Y ) }.
% 0.72/1.23 parent1[0]: (3417) {G2,W13,D3,L3,V3,M3} { distinct_lines( X,
% 0.72/1.23 parallel_through_point( Y, Z ) ), distinct_lines( parallel_through_point
% 0.72/1.23 ( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := parallel_through_point( Y, Z )
% 0.72/1.23 Y := X
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 factor: (3425) {G2,W8,D3,L2,V3,M2} { distinct_lines(
% 0.72/1.23 parallel_through_point( X, Y ), Z ), ! apart_point_and_line( Y, Z ) }.
% 0.72/1.23 parent0[0, 1]: (3423) {G2,W13,D3,L3,V3,M3} { distinct_lines(
% 0.72/1.23 parallel_through_point( Y, Z ), X ), distinct_lines(
% 0.72/1.23 parallel_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Z
% 0.72/1.23 Y := X
% 0.72/1.23 Z := Y
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (2399) {G3,W8,D3,L2,V3,M1} F(2391);r(56) { distinct_lines(
% 0.72/1.23 parallel_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.23 parent0: (3425) {G2,W8,D3,L2,V3,M2} { distinct_lines(
% 0.72/1.23 parallel_through_point( X, Y ), Z ), ! apart_point_and_line( Y, Z ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Y
% 0.72/1.23 Y := Z
% 0.72/1.23 Z := X
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 factor: (3428) {G2,W13,D3,L3,V3,M3} { distinct_lines( X,
% 0.72/1.23 orthogonal_through_point( Y, Z ) ), distinct_lines(
% 0.72/1.23 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.23 parent0[0, 2]: (2390) {G2,W14,D3,L4,V5,M1} R(131,142) { distinct_lines( X,
% 0.72/1.23 Y ), distinct_lines( Y, Z ), distinct_lines( Z, orthogonal_through_point
% 0.72/1.23 ( U, T ) ), ! apart_point_and_line( T, X ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := orthogonal_through_point( Y, Z )
% 0.72/1.23 Z := X
% 0.72/1.23 T := Z
% 0.72/1.23 U := Y
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (3434) {G2,W13,D3,L3,V3,M3} { distinct_lines(
% 0.72/1.23 orthogonal_through_point( Y, Z ), X ), distinct_lines(
% 0.72/1.23 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.23 parent0[0]: (56) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 0.72/1.23 distinct_lines( X, Y ) }.
% 0.72/1.23 parent1[0]: (3428) {G2,W13,D3,L3,V3,M3} { distinct_lines( X,
% 0.72/1.23 orthogonal_through_point( Y, Z ) ), distinct_lines(
% 0.72/1.23 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := orthogonal_through_point( Y, Z )
% 0.72/1.23 Y := X
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 factor: (3436) {G2,W8,D3,L2,V3,M2} { distinct_lines(
% 0.72/1.23 orthogonal_through_point( X, Y ), Z ), ! apart_point_and_line( Y, Z ) }.
% 0.72/1.23 parent0[0, 1]: (3434) {G2,W13,D3,L3,V3,M3} { distinct_lines(
% 0.72/1.23 orthogonal_through_point( Y, Z ), X ), distinct_lines(
% 0.72/1.23 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Z
% 0.72/1.23 Y := X
% 0.72/1.23 Z := Y
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (2400) {G3,W8,D3,L2,V3,M1} F(2390);r(56) { distinct_lines(
% 0.72/1.23 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.23 parent0: (3436) {G2,W8,D3,L2,V3,M2} { distinct_lines(
% 0.72/1.23 orthogonal_through_point( X, Y ), Z ), ! apart_point_and_line( Y, Z ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Y
% 0.72/1.23 Y := Z
% 0.72/1.23 Z := X
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (3439) {G1,W8,D3,L2,V1,M2} { distinct_lines(
% 0.72/1.23 orthogonal_through_point( X, skol1 ), skol3 ), apart_point_and_line(
% 0.72/1.23 skol1, skol2 ) }.
% 0.72/1.23 parent0[1]: (2400) {G3,W8,D3,L2,V3,M1} F(2390);r(56) { distinct_lines(
% 0.72/1.23 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.23 parent1[1]: (48) {G0,W6,D2,L2,V0,M1} I { apart_point_and_line( skol1, skol2
% 0.72/1.23 ), apart_point_and_line( skol1, skol3 ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := skol3
% 0.72/1.23 Y := X
% 0.72/1.23 Z := skol1
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (2421) {G4,W8,D3,L2,V1,M1} R(2400,48) { distinct_lines(
% 0.72/1.23 orthogonal_through_point( X, skol1 ), skol3 ), apart_point_and_line(
% 0.72/1.23 skol1, skol2 ) }.
% 0.72/1.23 parent0: (3439) {G1,W8,D3,L2,V1,M2} { distinct_lines(
% 0.72/1.23 orthogonal_through_point( X, skol1 ), skol3 ), apart_point_and_line(
% 0.72/1.23 skol1, skol2 ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (3440) {G4,W10,D3,L2,V2,M2} { distinct_lines(
% 0.72/1.23 parallel_through_point( X, skol1 ), skol2 ), distinct_lines(
% 0.72/1.23 orthogonal_through_point( Y, skol1 ), skol3 ) }.
% 0.72/1.23 parent0[1]: (2399) {G3,W8,D3,L2,V3,M1} F(2391);r(56) { distinct_lines(
% 0.72/1.23 parallel_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.23 parent1[1]: (2421) {G4,W8,D3,L2,V1,M1} R(2400,48) { distinct_lines(
% 0.72/1.23 orthogonal_through_point( X, skol1 ), skol3 ), apart_point_and_line(
% 0.72/1.23 skol1, skol2 ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := skol2
% 0.72/1.23 Y := X
% 0.72/1.23 Z := skol1
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := Y
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (2456) {G5,W10,D3,L2,V2,M1} R(2421,2399) { distinct_lines(
% 0.72/1.23 parallel_through_point( Y, skol1 ), skol2 ), distinct_lines(
% 0.72/1.23 orthogonal_through_point( X, skol1 ), skol3 ) }.
% 0.72/1.23 parent0: (3440) {G4,W10,D3,L2,V2,M2} { distinct_lines(
% 0.72/1.23 parallel_through_point( X, skol1 ), skol2 ), distinct_lines(
% 0.72/1.23 orthogonal_through_point( Y, skol1 ), skol3 ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Y
% 0.72/1.23 Y := X
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (3442) {G3,W10,D3,L2,V2,M2} { convergent_lines( skol3,
% 0.72/1.23 orthogonal_through_point( X, skol1 ) ), distinct_lines(
% 0.72/1.23 parallel_through_point( Y, skol1 ), skol2 ) }.
% 0.72/1.23 parent0[1]: (110) {G2,W6,D2,L2,V2,M1} R(14,56) { convergent_lines( X, Y ),
% 0.72/1.23 ! distinct_lines( Y, X ) }.
% 0.72/1.23 parent1[1]: (2456) {G5,W10,D3,L2,V2,M1} R(2421,2399) { distinct_lines(
% 0.72/1.23 parallel_through_point( Y, skol1 ), skol2 ), distinct_lines(
% 0.72/1.23 orthogonal_through_point( X, skol1 ), skol3 ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := skol3
% 0.72/1.23 Y := orthogonal_through_point( X, skol1 )
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (2793) {G6,W10,D3,L2,V2,M1} R(2456,110) { convergent_lines(
% 0.72/1.23 skol3, orthogonal_through_point( Y, skol1 ) ), distinct_lines(
% 0.72/1.23 parallel_through_point( X, skol1 ), skol2 ) }.
% 0.72/1.23 parent0: (3442) {G3,W10,D3,L2,V2,M2} { convergent_lines( skol3,
% 0.72/1.23 orthogonal_through_point( X, skol1 ) ), distinct_lines(
% 0.72/1.23 parallel_through_point( Y, skol1 ), skol2 ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Y
% 0.72/1.23 Y := X
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (3443) {G3,W10,D3,L2,V2,M2} { convergent_lines( skol2,
% 0.72/1.23 parallel_through_point( X, skol1 ) ), convergent_lines( skol3,
% 0.72/1.23 orthogonal_through_point( Y, skol1 ) ) }.
% 0.72/1.23 parent0[1]: (110) {G2,W6,D2,L2,V2,M1} R(14,56) { convergent_lines( X, Y ),
% 0.72/1.23 ! distinct_lines( Y, X ) }.
% 0.72/1.23 parent1[1]: (2793) {G6,W10,D3,L2,V2,M1} R(2456,110) { convergent_lines(
% 0.72/1.23 skol3, orthogonal_through_point( Y, skol1 ) ), distinct_lines(
% 0.72/1.23 parallel_through_point( X, skol1 ), skol2 ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := skol2
% 0.72/1.23 Y := parallel_through_point( X, skol1 )
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (2811) {G7,W10,D3,L2,V2,M1} R(2793,110) { convergent_lines(
% 0.72/1.23 skol3, orthogonal_through_point( X, skol1 ) ), convergent_lines( skol2,
% 0.72/1.23 parallel_through_point( Y, skol1 ) ) }.
% 0.72/1.23 parent0: (3443) {G3,W10,D3,L2,V2,M2} { convergent_lines( skol2,
% 0.72/1.23 parallel_through_point( X, skol1 ) ), convergent_lines( skol3,
% 0.72/1.23 orthogonal_through_point( Y, skol1 ) ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Y
% 0.72/1.23 Y := X
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 1
% 0.72/1.23 1 ==> 0
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (3444) {G7,W5,D3,L1,V1,M1} { convergent_lines( skol3,
% 0.72/1.23 orthogonal_through_point( Z, skol1 ) ) }.
% 0.72/1.23 parent0[0]: (246) {G6,W9,D5,L1,V4,M1} R(243,77) { ! convergent_lines( X,
% 0.72/1.23 parallel_through_point( parallel_through_point( parallel_through_point( X
% 0.72/1.23 , Y ), Z ), T ) ) }.
% 0.72/1.23 parent1[1]: (2811) {G7,W10,D3,L2,V2,M1} R(2793,110) { convergent_lines(
% 0.72/1.23 skol3, orthogonal_through_point( X, skol1 ) ), convergent_lines( skol2,
% 0.72/1.23 parallel_through_point( Y, skol1 ) ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := skol2
% 0.72/1.23 Y := X
% 0.72/1.23 Z := Y
% 0.72/1.23 T := skol1
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := Z
% 0.72/1.23 Y := parallel_through_point( parallel_through_point( skol2, X ), Y )
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (2821) {G8,W5,D3,L1,V1,M1} R(2811,246) { convergent_lines(
% 0.72/1.23 skol3, orthogonal_through_point( X, skol1 ) ) }.
% 0.72/1.23 parent0: (3444) {G7,W5,D3,L1,V1,M1} { convergent_lines( skol3,
% 0.72/1.23 orthogonal_through_point( Z, skol1 ) ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Y
% 0.72/1.23 Y := Z
% 0.72/1.23 Z := X
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (3445) {G2,W5,D3,L1,V1,M1} { convergent_lines(
% 0.72/1.23 orthogonal_through_point( X, skol1 ), skol3 ) }.
% 0.72/1.23 parent0[0]: (70) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.72/1.23 convergent_lines( X, Y ) }.
% 0.72/1.23 parent1[0]: (2821) {G8,W5,D3,L1,V1,M1} R(2811,246) { convergent_lines(
% 0.72/1.23 skol3, orthogonal_through_point( X, skol1 ) ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := orthogonal_through_point( X, skol1 )
% 0.72/1.23 Y := skol3
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := X
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (2834) {G9,W5,D3,L1,V1,M1} R(2821,70) { convergent_lines(
% 0.72/1.23 orthogonal_through_point( X, skol1 ), skol3 ) }.
% 0.72/1.23 parent0: (3445) {G2,W5,D3,L1,V1,M1} { convergent_lines(
% 0.72/1.23 orthogonal_through_point( X, skol1 ), skol3 ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (3446) {G1,W13,D3,L3,V3,M3} { ! convergent_lines( Z,
% 0.72/1.23 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ), !
% 0.72/1.23 unorthogonal_lines( Z, orthogonal_through_point( X, Y ) ) }.
% 0.72/1.23 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 0.72/1.23 orthogonal_through_point( Y, X ), Y ) }.
% 0.72/1.23 parent1[3]: (167) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y
% 0.72/1.23 ), convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 0.72/1.23 unorthogonal_lines( Y, Z ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Y
% 0.72/1.23 Y := X
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := Z
% 0.72/1.23 Y := orthogonal_through_point( X, Y )
% 0.72/1.23 Z := X
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (3447) {G2,W11,D3,L3,V3,M3} { convergent_lines( X, Y ), !
% 0.72/1.23 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ),
% 0.72/1.23 convergent_lines( X, Y ) }.
% 0.72/1.23 parent0[0]: (3446) {G1,W13,D3,L3,V3,M3} { ! convergent_lines( Z,
% 0.72/1.23 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ), !
% 0.72/1.23 unorthogonal_lines( Z, orthogonal_through_point( X, Y ) ) }.
% 0.72/1.23 parent1[0]: (200) {G4,W8,D3,L2,V3,M2} R(183,70) { convergent_lines( X,
% 0.72/1.23 orthogonal_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Y
% 0.72/1.23 Y := Z
% 0.72/1.23 Z := X
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 factor: (3448) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 0.72/1.23 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 0.72/1.23 parent0[0, 2]: (3447) {G2,W11,D3,L3,V3,M3} { convergent_lines( X, Y ), !
% 0.72/1.23 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ),
% 0.72/1.23 convergent_lines( X, Y ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (3103) {G5,W8,D3,L2,V3,M1} R(167,23);r(200) { convergent_lines
% 0.72/1.23 ( X, Y ), ! unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 0.72/1.23 parent0: (3448) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 0.72/1.23 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 1 ==> 1
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (3449) {G2,W10,D3,L2,V4,M2} { convergent_lines(
% 0.72/1.23 orthogonal_through_point( X, Y ), Z ), ! convergent_lines(
% 0.72/1.23 orthogonal_through_point( Z, T ), X ) }.
% 0.72/1.23 parent0[1]: (3103) {G5,W8,D3,L2,V3,M1} R(167,23);r(200) { convergent_lines
% 0.72/1.23 ( X, Y ), ! unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 0.72/1.23 parent1[1]: (258) {G1,W8,D3,L2,V3,M1} R(31,23) { ! convergent_lines( X, Y )
% 0.72/1.23 , unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := orthogonal_through_point( X, Y )
% 0.72/1.23 Y := Z
% 0.72/1.23 Z := T
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := orthogonal_through_point( Z, T )
% 0.72/1.23 Y := X
% 0.72/1.23 Z := Y
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (3110) {G6,W10,D3,L2,V4,M2} R(3103,258) { ! convergent_lines(
% 0.72/1.23 orthogonal_through_point( Z, T ), X ), convergent_lines(
% 0.72/1.23 orthogonal_through_point( X, Y ), Z ) }.
% 0.72/1.23 parent0: (3449) {G2,W10,D3,L2,V4,M2} { convergent_lines(
% 0.72/1.23 orthogonal_through_point( X, Y ), Z ), ! convergent_lines(
% 0.72/1.23 orthogonal_through_point( Z, T ), X ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := X
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 T := T
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 1
% 0.72/1.23 1 ==> 0
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (3450) {G7,W5,D3,L1,V2,M1} { convergent_lines(
% 0.72/1.23 orthogonal_through_point( skol3, Y ), X ) }.
% 0.72/1.23 parent0[0]: (3110) {G6,W10,D3,L2,V4,M2} R(3103,258) { ! convergent_lines(
% 0.72/1.23 orthogonal_through_point( Z, T ), X ), convergent_lines(
% 0.72/1.23 orthogonal_through_point( X, Y ), Z ) }.
% 0.72/1.23 parent1[0]: (2834) {G9,W5,D3,L1,V1,M1} R(2821,70) { convergent_lines(
% 0.72/1.23 orthogonal_through_point( X, skol1 ), skol3 ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := skol3
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := X
% 0.72/1.23 T := skol1
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := X
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (3125) {G10,W5,D3,L1,V2,M1} R(3110,2834) { convergent_lines(
% 0.72/1.23 orthogonal_through_point( skol3, X ), Y ) }.
% 0.72/1.23 parent0: (3450) {G7,W5,D3,L1,V2,M1} { convergent_lines(
% 0.72/1.23 orthogonal_through_point( skol3, Y ), X ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := Y
% 0.72/1.23 Y := X
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 0 ==> 0
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 resolution: (3451) {G7,W0,D0,L0,V0,M0} { }.
% 0.72/1.23 parent0[0]: (246) {G6,W9,D5,L1,V4,M1} R(243,77) { ! convergent_lines( X,
% 0.72/1.23 parallel_through_point( parallel_through_point( parallel_through_point( X
% 0.72/1.23 , Y ), Z ), T ) ) }.
% 0.72/1.23 parent1[0]: (3125) {G10,W5,D3,L1,V2,M1} R(3110,2834) { convergent_lines(
% 0.72/1.23 orthogonal_through_point( skol3, X ), Y ) }.
% 0.72/1.23 substitution0:
% 0.72/1.23 X := orthogonal_through_point( skol3, X )
% 0.72/1.23 Y := Y
% 0.72/1.23 Z := Z
% 0.72/1.23 T := T
% 0.72/1.23 end
% 0.72/1.23 substitution1:
% 0.72/1.23 X := X
% 0.72/1.23 Y := parallel_through_point( parallel_through_point(
% 0.72/1.23 parallel_through_point( orthogonal_through_point( skol3, X ), Y ), Z ), T
% 0.72/1.23 )
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 subsumption: (3208) {G11,W0,D0,L0,V0,M0} R(3125,246) { }.
% 0.72/1.23 parent0: (3451) {G7,W0,D0,L0,V0,M0} { }.
% 0.72/1.23 substitution0:
% 0.72/1.23 end
% 0.72/1.23 permutation0:
% 0.72/1.23 end
% 0.72/1.23
% 0.72/1.23 Proof check complete!
% 0.72/1.23
% 0.72/1.23 Memory use:
% 0.72/1.23
% 0.72/1.23 space for terms: 42316
% 0.72/1.23 space for clauses: 124918
% 0.72/1.23
% 0.72/1.23
% 0.72/1.23 clauses generated: 16763
% 0.72/1.23 clauses kept: 3209
% 0.72/1.23 clauses selected: 429
% 0.72/1.23 clauses deleted: 8
% 0.72/1.23 clauses inuse deleted: 7
% 0.72/1.23
% 0.72/1.23 subsentry: 201770
% 0.72/1.23 literals s-matched: 92768
% 0.72/1.23 literals matched: 92698
% 0.72/1.23 full subsumption: 58266
% 0.72/1.23
% 0.72/1.23 checksum: 818211123
% 0.72/1.23
% 0.72/1.23
% 0.72/1.23 Bliksem ended
%------------------------------------------------------------------------------