%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO185+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n032.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 02:52:25 EDT 2022
% Result : Theorem 0.72s 1.08s
% Output : Refutation 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : GEO185+3 : TPTP v8.1.0. Released v4.0.0.
% 0.02/0.09 % Command : bliksem %s
% 0.10/0.28 % Computer : n032.cluster.edu
% 0.10/0.28 % Model : x86_64 x86_64
% 0.10/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.28 % Memory : 8042.1875MB
% 0.10/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.28 % CPULimit : 300
% 0.10/0.28 % DateTime : Sat Jun 18 17:13:47 EDT 2022
% 0.10/0.28 % CPUTime :
% 0.72/1.08 *** allocated 10000 integers for termspace/termends
% 0.72/1.08 *** allocated 10000 integers for clauses
% 0.72/1.08 *** allocated 10000 integers for justifications
% 0.72/1.08 Bliksem 1.12
% 0.72/1.08
% 0.72/1.08
% 0.72/1.08 Automatic Strategy Selection
% 0.72/1.08
% 0.72/1.08
% 0.72/1.08 Clauses:
% 0.72/1.08
% 0.72/1.08 { ! distinct_points( X, X ) }.
% 0.72/1.08 { ! distinct_lines( X, X ) }.
% 0.72/1.08 { ! convergent_lines( X, X ) }.
% 0.72/1.08 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 0.72/1.08 ) }.
% 0.72/1.08 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.72/1.08 }.
% 0.72/1.08 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 0.72/1.08 , Z ) }.
% 0.72/1.08 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 0.72/1.08 , Y ) ) }.
% 0.72/1.08 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 0.72/1.08 , Y ) ) }.
% 0.72/1.08 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.72/1.08 , Y ), X ) }.
% 0.72/1.08 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.72/1.08 , Y ), Y ) }.
% 0.72/1.08 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 0.72/1.08 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 0.72/1.08 apart_point_and_line( Y, T ) }.
% 0.72/1.08 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 0.72/1.08 apart_point_and_line( Z, Y ) }.
% 0.72/1.08 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 0.72/1.08 apart_point_and_line( X, Z ) }.
% 0.72/1.08 { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X,
% 0.72/1.08 Z ) }.
% 0.72/1.08 { ! distinct_lines( X, Y ), convergent_lines( X, Y ) }.
% 0.72/1.08 { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 0.72/1.08 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 0.72/1.08 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 0.72/1.08 apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 0.72/1.08 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.72/1.08 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.72/1.08 , convergent_lines( Y, Z ) }.
% 0.72/1.08 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.72/1.08 , unorthogonal_lines( Y, Z ) }.
% 0.72/1.08 { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 0.72/1.08 { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.72/1.08 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 0.72/1.08 }.
% 0.72/1.08 { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 0.72/1.08 { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 0.72/1.08 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 0.72/1.08 apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ),
% 0.72/1.08 unorthogonal_lines( Y, T ) }.
% 0.72/1.08 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.72/1.08 { alpha2( X, Z ), convergent_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 0.72/1.08 unorthogonal_lines( X, Y ) }.
% 0.72/1.08 { alpha2( X, Z ), unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 0.72/1.08 unorthogonal_lines( X, Y ) }.
% 0.72/1.08 { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 0.72/1.08 { ! alpha2( X, Y ), unorthogonal_lines( Y, X ) }.
% 0.72/1.08 { ! convergent_lines( Y, X ), ! unorthogonal_lines( Y, X ), alpha2( X, Y )
% 0.72/1.08 }.
% 0.72/1.08 { unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ), !
% 0.72/1.08 convergent_lines( X, Y ) }.
% 0.72/1.08 { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line(
% 0.72/1.08 line_connecting( X, Y ) ) }.
% 0.72/1.08 { ! line( X ), ! line( Y ), ! convergent_lines( X, Y ), point(
% 0.72/1.08 intersection_point( X, Y ) ) }.
% 0.72/1.08 { ! line( X ), ! point( Y ), line( parallel_through_point( X, Y ) ) }.
% 0.72/1.08 { ! line( X ), ! point( Y ), line( orthogonal_through_point( X, Y ) ) }.
% 0.72/1.08 { ! equal_points( X, Y ), ! distinct_points( X, Y ) }.
% 0.72/1.08 { distinct_points( X, Y ), equal_points( X, Y ) }.
% 0.72/1.08 { ! equal_lines( X, Y ), ! distinct_lines( X, Y ) }.
% 0.72/1.08 { distinct_lines( X, Y ), equal_lines( X, Y ) }.
% 0.72/1.08 { ! parallel_lines( X, Y ), ! convergent_lines( X, Y ) }.
% 0.72/1.08 { convergent_lines( X, Y ), parallel_lines( X, Y ) }.
% 0.72/1.08 { ! incident_point_and_line( X, Y ), ! apart_point_and_line( X, Y ) }.
% 0.72/1.08 { apart_point_and_line( X, Y ), incident_point_and_line( X, Y ) }.
% 0.72/1.08 { ! orthogonal_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.72/1.08 { unorthogonal_lines( X, Y ), orthogonal_lines( X, Y ) }.
% 0.72/1.08 { distinct_points( skol1, skol4 ) }.
% 0.72/1.08 { convergent_lines( skol2, skol3 ) }.
% 0.72/1.08 { equal_points( skol1, intersection_point( skol2, skol3 ) ) }.
% 0.72/1.08 { ! incident_point_and_line( skol1, skol2 ), ! incident_point_and_line(
% 0.72/1.08 skol1, skol3 ) }.
% 0.72/1.08
% 0.72/1.08 percentage equality = 0.000000, percentage horn = 0.620000
% 0.72/1.08 This a non-horn, non-equality problem
% 0.72/1.08
% 0.72/1.08
% 0.72/1.08 Options Used:
% 0.72/1.08
% 0.72/1.08 useres = 1
% 0.72/1.08 useparamod = 0
% 0.72/1.08 useeqrefl = 0
% 0.72/1.08 useeqfact = 0
% 0.72/1.08 usefactor = 1
% 0.72/1.08 usesimpsplitting = 0
% 0.72/1.08 usesimpdemod = 0
% 0.72/1.08 usesimpres = 3
% 0.72/1.08
% 0.72/1.08 resimpinuse = 1000
% 0.72/1.08 resimpclauses = 20000
% 0.72/1.08 substype = standard
% 0.72/1.08 backwardsubs = 1
% 0.72/1.08 selectoldest = 5
% 0.72/1.08
% 0.72/1.08 litorderings [0] = split
% 0.72/1.08 litorderings [1] = liftord
% 0.72/1.08
% 0.72/1.08 termordering = none
% 0.72/1.08
% 0.72/1.08 litapriori = 1
% 0.72/1.08 termapriori = 0
% 0.72/1.08 litaposteriori = 0
% 0.72/1.08 termaposteriori = 0
% 0.72/1.08 demodaposteriori = 0
% 0.72/1.08 ordereqreflfact = 0
% 0.72/1.08
% 0.72/1.08 litselect = none
% 0.72/1.08
% 0.72/1.08 maxweight = 15
% 0.72/1.08 maxdepth = 30000
% 0.72/1.08 maxlength = 115
% 0.72/1.08 maxnrvars = 195
% 0.72/1.08 excuselevel = 1
% 0.72/1.08 increasemaxweight = 1
% 0.72/1.08
% 0.72/1.08 maxselected = 10000000
% 0.72/1.08 maxnrclauses = 10000000
% 0.72/1.08
% 0.72/1.08 showgenerated = 0
% 0.72/1.08 showkept = 0
% 0.72/1.08 showselected = 0
% 0.72/1.08 showdeleted = 0
% 0.72/1.08 showresimp = 1
% 0.72/1.08 showstatus = 2000
% 0.72/1.08
% 0.72/1.08 prologoutput = 0
% 0.72/1.08 nrgoals = 5000000
% 0.72/1.08 totalproof = 1
% 0.72/1.08
% 0.72/1.08 Symbols occurring in the translation:
% 0.72/1.08
% 0.72/1.08 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.72/1.08 . [1, 2] (w:1, o:27, a:1, s:1, b:0),
% 0.72/1.08 ! [4, 1] (w:0, o:20, a:1, s:1, b:0),
% 0.72/1.08 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.72/1.08 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.72/1.08 distinct_points [36, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.72/1.08 distinct_lines [37, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.72/1.08 convergent_lines [38, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.72/1.08 line_connecting [41, 2] (w:1, o:54, a:1, s:1, b:0),
% 0.72/1.08 apart_point_and_line [42, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.72/1.08 intersection_point [43, 2] (w:1, o:56, a:1, s:1, b:0),
% 0.72/1.08 parallel_through_point [46, 2] (w:1, o:59, a:1, s:1, b:0),
% 0.72/1.08 unorthogonal_lines [49, 2] (w:1, o:60, a:1, s:1, b:0),
% 0.72/1.08 orthogonal_through_point [52, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.72/1.08 point [54, 1] (w:1, o:25, a:1, s:1, b:0),
% 0.72/1.08 line [55, 1] (w:1, o:26, a:1, s:1, b:0),
% 0.72/1.08 equal_points [56, 2] (w:1, o:61, a:1, s:1, b:0),
% 0.72/1.08 equal_lines [57, 2] (w:1, o:62, a:1, s:1, b:0),
% 0.72/1.08 parallel_lines [58, 2] (w:1, o:63, a:1, s:1, b:0),
% 0.72/1.08 incident_point_and_line [59, 2] (w:1, o:64, a:1, s:1, b:0),
% 0.72/1.08 orthogonal_lines [60, 2] (w:1, o:58, a:1, s:1, b:0),
% 0.72/1.08 alpha1 [61, 2] (w:1, o:65, a:1, s:1, b:0),
% 0.72/1.08 alpha2 [62, 2] (w:1, o:66, a:1, s:1, b:0),
% 0.72/1.08 skol1 [63, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.72/1.08 skol2 [64, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.72/1.08 skol3 [65, 0] (w:1, o:18, a:1, s:1, b:0),
% 0.72/1.08 skol4 [66, 0] (w:1, o:19, a:1, s:1, b:0).
% 0.72/1.08
% 0.72/1.08
% 0.72/1.08 Starting Search:
% 0.72/1.08
% 0.72/1.08 *** allocated 15000 integers for clauses
% 0.72/1.08 *** allocated 22500 integers for clauses
% 0.72/1.08 *** allocated 33750 integers for clauses
% 0.72/1.08 *** allocated 15000 integers for termspace/termends
% 0.72/1.08 *** allocated 50625 integers for clauses
% 0.72/1.08 Resimplifying inuse:
% 0.72/1.08 Done
% 0.72/1.08
% 0.72/1.08 *** allocated 22500 integers for termspace/termends
% 0.72/1.08 *** allocated 75937 integers for clauses
% 0.72/1.08 *** allocated 33750 integers for termspace/termends
% 0.72/1.08 *** allocated 113905 integers for clauses
% 0.72/1.08
% 0.72/1.08 Intermediate Status:
% 0.72/1.08 Generated: 10607
% 0.72/1.08 Kept: 2077
% 0.72/1.08 Inuse: 328
% 0.72/1.08 Deleted: 1
% 0.72/1.08 Deletedinuse: 0
% 0.72/1.08
% 0.72/1.08 Resimplifying inuse:
% 0.72/1.08 Done
% 0.72/1.08
% 0.72/1.08 *** allocated 50625 integers for termspace/termends
% 0.72/1.08 *** allocated 170857 integers for clauses
% 0.72/1.08 Resimplifying inuse:
% 0.72/1.08 Done
% 0.72/1.08
% 0.72/1.08 *** allocated 75937 integers for termspace/termends
% 0.72/1.08
% 0.72/1.08 Bliksems!, er is een bewijs:
% 0.72/1.08 % SZS status Theorem
% 0.72/1.08 % SZS output start Refutation
% 0.72/1.08
% 0.72/1.08 (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.72/1.08 (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.72/1.08 (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.72/1.08 , ! distinct_lines( X, Y ) }.
% 0.72/1.08 (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), convergent_lines( Y,
% 0.72/1.08 Z ), ! convergent_lines( X, Y ) }.
% 0.72/1.08 (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), apart_point_and_line(
% 0.72/1.08 X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.72/1.08 (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! distinct_lines( X
% 0.72/1.08 , Y ) }.
% 0.72/1.08 (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines( parallel_through_point( Y
% 0.72/1.08 , X ), Y ) }.
% 0.72/1.08 (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.72/1.08 parallel_through_point( Y, X ) ) }.
% 0.72/1.08 (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), unorthogonal_lines(
% 0.72/1.08 X, Y ) }.
% 0.72/1.08 (18) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 0.72/1.08 unorthogonal_lines( X, Y ), convergent_lines( Y, Z ), alpha1( X, Z ) }.
% 0.72/1.08 (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 0.72/1.08 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 0.72/1.08 }.
% 0.72/1.08 (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! alpha1( X, Y ) }.
% 0.72/1.08 (21) {G0,W6,D2,L2,V2,M1} I { unorthogonal_lines( X, Y ), ! alpha1( X, Y )
% 0.72/1.08 }.
% 0.72/1.08 (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( orthogonal_through_point
% 0.72/1.08 ( Y, X ), Y ) }.
% 0.72/1.08 (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.72/1.08 orthogonal_through_point( Y, X ) ) }.
% 0.72/1.08 (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ), unorthogonal_lines
% 0.72/1.08 ( Z, X ), unorthogonal_lines( Z, Y ) }.
% 0.72/1.08 (43) {G0,W6,D2,L2,V2,M1} I { apart_point_and_line( X, Y ),
% 0.72/1.08 incident_point_and_line( X, Y ) }.
% 0.72/1.08 (49) {G0,W6,D2,L2,V0,M1} I { ! incident_point_and_line( skol1, skol2 ), !
% 0.72/1.08 incident_point_and_line( skol1, skol3 ) }.
% 0.72/1.08 (56) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 0.72/1.08 ( X, Y ) }.
% 0.72/1.08 (67) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.72/1.08 convergent_lines( X, Y ) }.
% 0.72/1.08 (68) {G2,W9,D2,L3,V3,M3} R(67,5) { convergent_lines( Z, X ), !
% 0.72/1.08 convergent_lines( Y, Z ), convergent_lines( X, Y ) }.
% 0.72/1.08 (70) {G2,W5,D3,L1,V2,M1} R(67,15) { ! convergent_lines( X,
% 0.72/1.08 parallel_through_point( X, Y ) ) }.
% 0.72/1.08 (72) {G3,W8,D3,L2,V3,M2} R(70,5) { ! convergent_lines( Y, X ),
% 0.72/1.08 convergent_lines( X, parallel_through_point( Y, Z ) ) }.
% 0.72/1.08 (108) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 0.72/1.08 orthogonal_through_point( X, Y ), X ) }.
% 0.72/1.08 (110) {G2,W8,D3,L2,V3,M2} R(108,5) { convergent_lines( X, Z ),
% 0.72/1.08 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.72/1.08 (122) {G2,W6,D2,L2,V2,M1} R(14,56) { convergent_lines( X, Y ), !
% 0.72/1.08 distinct_lines( Y, X ) }.
% 0.72/1.08 (132) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ),
% 0.72/1.08 distinct_lines( Y, T ), apart_point_and_line( Z, T ), !
% 0.72/1.08 apart_point_and_line( Z, X ) }.
% 0.72/1.08 (142) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X,
% 0.72/1.08 parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.08 (143) {G1,W8,D3,L2,V3,M1} R(12,24) { distinct_lines( X,
% 0.72/1.08 orthogonal_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.08 (159) {G1,W12,D2,L4,V3,M2} R(18,21) { ! convergent_lines( X, Y ),
% 0.72/1.08 convergent_lines( Y, Z ), unorthogonal_lines( X, Z ), !
% 0.72/1.08 unorthogonal_lines( X, Y ) }.
% 0.72/1.08 (165) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y ),
% 0.72/1.08 convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 0.72/1.08 unorthogonal_lines( Y, Z ) }.
% 0.72/1.08 (166) {G1,W12,D2,L4,V3,M3} R(19,21) { ! convergent_lines( X, Y ),
% 0.72/1.08 unorthogonal_lines( Y, Z ), unorthogonal_lines( X, Z ), !
% 0.72/1.08 unorthogonal_lines( X, Y ) }.
% 0.72/1.08 (167) {G1,W6,D2,L2,V0,M1} R(49,43) { apart_point_and_line( skol1, skol3 ),
% 0.72/1.08 ! incident_point_and_line( skol1, skol2 ) }.
% 0.72/1.08 (168) {G2,W6,D2,L2,V0,M1} R(167,43) { apart_point_and_line( skol1, skol2 )
% 0.72/1.08 , apart_point_and_line( skol1, skol3 ) }.
% 0.72/1.08 (190) {G3,W8,D3,L2,V3,M2} R(110,67) { convergent_lines( Z, X ),
% 0.72/1.08 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.72/1.08 (203) {G4,W8,D3,L2,V3,M2} R(190,67) { convergent_lines( X,
% 0.72/1.08 orthogonal_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 0.72/1.08 (236) {G4,W7,D4,L1,V3,M1} R(72,15) { ! convergent_lines( X,
% 0.72/1.08 parallel_through_point( parallel_through_point( X, Y ), Z ) ) }.
% 0.72/1.08 (246) {G5,W7,D4,L1,V3,M1} R(236,67) { ! convergent_lines(
% 0.72/1.08 parallel_through_point( parallel_through_point( X, Y ), Z ), X ) }.
% 0.72/1.08 (249) {G6,W9,D5,L1,V4,M1} R(246,72) { ! convergent_lines( X,
% 0.72/1.08 parallel_through_point( parallel_through_point( parallel_through_point( X
% 0.72/1.08 , Y ), Z ), T ) ) }.
% 0.72/1.08 (257) {G1,W8,D3,L2,V3,M1} R(31,23) { ! convergent_lines( X, Y ),
% 0.72/1.08 unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 0.72/1.08 (2371) {G2,W14,D3,L4,V5,M1} R(132,143) { distinct_lines( X, Y ),
% 0.72/1.08 distinct_lines( Y, Z ), distinct_lines( Z, orthogonal_through_point( U, T
% 0.72/1.08 ) ), ! apart_point_and_line( T, X ) }.
% 0.72/1.08 (2372) {G2,W14,D3,L4,V5,M1} R(132,142) { distinct_lines( X, Y ),
% 0.72/1.08 distinct_lines( Y, Z ), distinct_lines( Z, parallel_through_point( U, T )
% 0.72/1.08 ), ! apart_point_and_line( T, X ) }.
% 0.72/1.08 (2380) {G3,W8,D3,L2,V3,M1} F(2372);r(56) { distinct_lines(
% 0.72/1.08 parallel_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.08 (2381) {G3,W8,D3,L2,V3,M1} F(2371);r(56) { distinct_lines(
% 0.72/1.08 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.08 (2402) {G4,W8,D3,L2,V1,M1} R(2381,168) { distinct_lines(
% 0.72/1.08 orthogonal_through_point( X, skol1 ), skol3 ), apart_point_and_line(
% 0.72/1.08 skol1, skol2 ) }.
% 0.72/1.08 (2437) {G5,W10,D3,L2,V2,M1} R(2402,2380) { distinct_lines(
% 0.72/1.08 parallel_through_point( Y, skol1 ), skol2 ), distinct_lines(
% 0.72/1.08 orthogonal_through_point( X, skol1 ), skol3 ) }.
% 0.72/1.08 (2840) {G6,W10,D3,L2,V2,M1} R(2437,122) { convergent_lines( skol3,
% 0.72/1.08 orthogonal_through_point( Y, skol1 ) ), distinct_lines(
% 0.72/1.08 parallel_through_point( X, skol1 ), skol2 ) }.
% 0.72/1.08 (2858) {G7,W10,D3,L2,V2,M1} R(2840,122) { convergent_lines( skol3,
% 0.72/1.08 orthogonal_through_point( X, skol1 ) ), convergent_lines( skol2,
% 0.72/1.08 parallel_through_point( Y, skol1 ) ) }.
% 0.72/1.08 (2868) {G8,W5,D3,L1,V1,M1} R(2858,249) { convergent_lines( skol3,
% 0.72/1.08 orthogonal_through_point( X, skol1 ) ) }.
% 0.72/1.08 (2873) {G9,W8,D3,L2,V2,M2} R(2868,68) { convergent_lines( Y, skol3 ),
% 0.72/1.08 convergent_lines( orthogonal_through_point( X, skol1 ), Y ) }.
% 0.72/1.08 (3021) {G4,W8,D3,L2,V3,M1} R(159,23);r(190) { convergent_lines( Z, X ), !
% 0.72/1.08 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.72/1.08 (3044) {G5,W8,D3,L2,V3,M1} R(165,23);r(203) { convergent_lines( X, Y ), !
% 0.72/1.08 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 0.72/1.08 (3051) {G6,W10,D3,L2,V4,M2} R(3044,257) { ! convergent_lines(
% 0.72/1.08 orthogonal_through_point( Z, T ), X ), convergent_lines(
% 0.72/1.08 orthogonal_through_point( X, Y ), Z ) }.
% 0.72/1.08 (3068) {G2,W15,D2,L5,V4,M3} R(166,31) { ! convergent_lines( X, Y ), !
% 0.72/1.08 convergent_lines( Y, T ), unorthogonal_lines( Y, Z ), unorthogonal_lines
% 0.72/1.08 ( X, T ), unorthogonal_lines( X, Z ) }.
% 0.72/1.08 (3079) {G3,W9,D2,L3,V3,M2} F(3068);r(17) { ! convergent_lines( X, Y ),
% 0.72/1.08 unorthogonal_lines( X, Z ), unorthogonal_lines( Y, Z ) }.
% 0.72/1.08 (3092) {G4,W8,D3,L2,V3,M1} R(3079,23) { ! convergent_lines(
% 0.72/1.08 orthogonal_through_point( X, Y ), Z ), unorthogonal_lines( Z, X ) }.
% 0.72/1.08 (3093) {G4,W8,D3,L2,V3,M1} R(3079,23) { ! convergent_lines( X,
% 0.72/1.08 orthogonal_through_point( Y, Z ) ), unorthogonal_lines( X, Y ) }.
% 0.72/1.08 (3138) {G5,W7,D3,L1,V3,M1} R(3092,23) { ! convergent_lines(
% 0.72/1.08 orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ) }.
% 0.72/1.08 (3140) {G10,W5,D3,L1,V2,M1} R(3138,2873) { convergent_lines(
% 0.72/1.08 orthogonal_through_point( X, Y ), skol3 ) }.
% 0.72/1.08 (3353) {G5,W10,D3,L2,V4,M2} R(3093,3021) { convergent_lines( Z, X ), !
% 0.72/1.08 convergent_lines( orthogonal_through_point( X, Y ),
% 0.72/1.08 orthogonal_through_point( Z, T ) ) }.
% 0.72/1.08 (3499) {G6,W9,D4,L1,V4,M1} R(3353,15) { ! convergent_lines(
% 0.72/1.08 orthogonal_through_point( X, Y ), orthogonal_through_point(
% 0.72/1.08 parallel_through_point( X, Z ), T ) ) }.
% 0.72/1.08 (3849) {G11,W5,D3,L1,V2,M1} R(3051,3140) { convergent_lines(
% 0.72/1.08 orthogonal_through_point( skol3, X ), Y ) }.
% 0.72/1.08 (3908) {G12,W0,D0,L0,V0,M0} R(3849,3499) { }.
% 0.72/1.08
% 0.72/1.08
% 0.72/1.08 % SZS output end Refutation
% 0.72/1.08 found a proof!
% 0.72/1.08
% 0.72/1.08
% 0.72/1.08 Unprocessed initial clauses:
% 0.72/1.08
% 0.72/1.08 (3910) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 0.72/1.08 (3911) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.72/1.08 (3912) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 0.72/1.08 (3913) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 0.72/1.08 , Z ), distinct_points( Y, Z ) }.
% 0.72/1.08 (3914) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X,
% 0.72/1.08 Z ), distinct_lines( Y, Z ) }.
% 0.72/1.08 (3915) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines
% 0.72/1.08 ( X, Z ), convergent_lines( Y, Z ) }.
% 0.72/1.08 (3916) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.72/1.08 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 0.72/1.08 (3917) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.72/1.08 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 0.72/1.08 (3918) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 0.72/1.08 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 0.72/1.08 (3919) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 0.72/1.08 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 0.72/1.08 (3920) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines
% 0.72/1.08 ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 0.72/1.08 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 0.72/1.08 (3921) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 0.72/1.08 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 0.72/1.08 (3922) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 0.72/1.08 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 0.72/1.08 (3923) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), distinct_lines( Y
% 0.72/1.08 , Z ), convergent_lines( X, Z ) }.
% 0.72/1.08 (3924) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ), convergent_lines( X
% 0.72/1.08 , Y ) }.
% 0.72/1.08 (3925) {G0,W5,D3,L1,V2,M1} { ! convergent_lines( parallel_through_point( Y
% 0.72/1.08 , X ), Y ) }.
% 0.72/1.08 (3926) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.72/1.08 parallel_through_point( Y, X ) ) }.
% 0.72/1.08 (3927) {G0,W12,D2,L4,V3,M4} { ! distinct_lines( X, Y ),
% 0.72/1.08 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 0.72/1.08 convergent_lines( X, Y ) }.
% 0.72/1.08 (3928) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines
% 0.72/1.08 ( X, Y ) }.
% 0.72/1.08 (3929) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.72/1.08 unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 0.72/1.08 (3930) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.72/1.08 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 0.72/1.08 }.
% 0.72/1.08 (3931) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines( X, Y )
% 0.72/1.08 }.
% 0.72/1.08 (3932) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 0.72/1.08 }.
% 0.72/1.08 (3933) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( X, Y ), !
% 0.72/1.08 unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 0.72/1.08 (3934) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines(
% 0.72/1.08 orthogonal_through_point( Y, X ), Y ) }.
% 0.72/1.08 (3935) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.72/1.08 orthogonal_through_point( Y, X ) ) }.
% 0.72/1.08 (3936) {G0,W15,D2,L5,V4,M5} { ! distinct_lines( X, Y ),
% 0.72/1.08 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 0.72/1.08 unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 0.72/1.08 (3937) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines
% 0.72/1.08 ( X, Y ) }.
% 0.72/1.08 (3938) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), convergent_lines( Z, Y ), !
% 0.72/1.08 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.72/1.08 (3939) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), unorthogonal_lines( Z, Y ),
% 0.72/1.08 ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.72/1.08 (3940) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), convergent_lines( Y, X )
% 0.72/1.08 }.
% 0.72/1.08 (3941) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), unorthogonal_lines( Y, X )
% 0.72/1.08 }.
% 0.72/1.08 (3942) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( Y, X ), !
% 0.72/1.08 unorthogonal_lines( Y, X ), alpha2( X, Y ) }.
% 0.72/1.08 (3943) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ),
% 0.72/1.08 unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 0.72/1.08 (3944) {G0,W11,D3,L4,V2,M4} { ! point( X ), ! point( Y ), !
% 0.72/1.08 distinct_points( X, Y ), line( line_connecting( X, Y ) ) }.
% 0.72/1.08 (3945) {G0,W11,D3,L4,V2,M4} { ! line( X ), ! line( Y ), ! convergent_lines
% 0.72/1.08 ( X, Y ), point( intersection_point( X, Y ) ) }.
% 0.72/1.08 (3946) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 0.72/1.08 parallel_through_point( X, Y ) ) }.
% 0.72/1.08 (3947) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 0.72/1.08 orthogonal_through_point( X, Y ) ) }.
% 0.72/1.08 (3948) {G0,W6,D2,L2,V2,M2} { ! equal_points( X, Y ), ! distinct_points( X
% 0.72/1.08 , Y ) }.
% 0.72/1.08 (3949) {G0,W6,D2,L2,V2,M2} { distinct_points( X, Y ), equal_points( X, Y )
% 0.72/1.08 }.
% 0.72/1.08 (3950) {G0,W6,D2,L2,V2,M2} { ! equal_lines( X, Y ), ! distinct_lines( X, Y
% 0.72/1.08 ) }.
% 0.72/1.08 (3951) {G0,W6,D2,L2,V2,M2} { distinct_lines( X, Y ), equal_lines( X, Y )
% 0.72/1.08 }.
% 0.72/1.08 (3952) {G0,W6,D2,L2,V2,M2} { ! parallel_lines( X, Y ), ! convergent_lines
% 0.72/1.08 ( X, Y ) }.
% 0.72/1.08 (3953) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), parallel_lines( X,
% 0.72/1.08 Y ) }.
% 0.72/1.08 (3954) {G0,W6,D2,L2,V2,M2} { ! incident_point_and_line( X, Y ), !
% 0.72/1.08 apart_point_and_line( X, Y ) }.
% 0.72/1.08 (3955) {G0,W6,D2,L2,V2,M2} { apart_point_and_line( X, Y ),
% 0.72/1.08 incident_point_and_line( X, Y ) }.
% 0.72/1.08 (3956) {G0,W6,D2,L2,V2,M2} { ! orthogonal_lines( X, Y ), !
% 0.72/1.08 unorthogonal_lines( X, Y ) }.
% 0.72/1.08 (3957) {G0,W6,D2,L2,V2,M2} { unorthogonal_lines( X, Y ), orthogonal_lines
% 0.72/1.08 ( X, Y ) }.
% 0.72/1.08 (3958) {G0,W3,D2,L1,V0,M1} { distinct_points( skol1, skol4 ) }.
% 0.72/1.08 (3959) {G0,W3,D2,L1,V0,M1} { convergent_lines( skol2, skol3 ) }.
% 0.72/1.08 (3960) {G0,W5,D3,L1,V0,M1} { equal_points( skol1, intersection_point(
% 0.72/1.08 skol2, skol3 ) ) }.
% 0.72/1.08 (3961) {G0,W6,D2,L2,V0,M2} { ! incident_point_and_line( skol1, skol2 ), !
% 0.72/1.08 incident_point_and_line( skol1, skol3 ) }.
% 0.72/1.08
% 0.72/1.08
% 0.72/1.08 Total Proof:
% 0.72/1.08
% 0.72/1.08 subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.72/1.08 parent0: (3911) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := X
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 0 ==> 0
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 subsumption: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.72/1.08 parent0: (3912) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := X
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 0 ==> 0
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 0.72/1.08 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 0.72/1.08 parent0: (3914) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ),
% 0.72/1.08 distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := X
% 0.72/1.08 Y := Y
% 0.72/1.08 Z := Z
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 0 ==> 2
% 0.72/1.08 1 ==> 0
% 0.72/1.08 2 ==> 1
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 subsumption: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 0.72/1.08 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.72/1.08 parent0: (3915) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 0.72/1.08 convergent_lines( X, Z ), convergent_lines( Y, Z ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := X
% 0.72/1.08 Y := Y
% 0.72/1.08 Z := Z
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 0 ==> 2
% 0.72/1.08 1 ==> 0
% 0.72/1.08 2 ==> 1
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 subsumption: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 0.72/1.08 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.72/1.08 parent0: (3922) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 0.72/1.08 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := X
% 0.72/1.08 Y := Y
% 0.72/1.08 Z := Z
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 0 ==> 2
% 0.72/1.08 1 ==> 0
% 0.72/1.08 2 ==> 1
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 subsumption: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 0.72/1.08 distinct_lines( X, Y ) }.
% 0.72/1.08 parent0: (3924) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ),
% 0.72/1.08 convergent_lines( X, Y ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := X
% 0.72/1.08 Y := Y
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 0 ==> 1
% 0.72/1.08 1 ==> 0
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 subsumption: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 0.72/1.08 parallel_through_point( Y, X ), Y ) }.
% 0.72/1.08 parent0: (3925) {G0,W5,D3,L1,V2,M1} { ! convergent_lines(
% 0.72/1.08 parallel_through_point( Y, X ), Y ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := X
% 0.72/1.08 Y := Y
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 0 ==> 0
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 subsumption: (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.72/1.08 parallel_through_point( Y, X ) ) }.
% 0.72/1.08 parent0: (3926) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.72/1.08 parallel_through_point( Y, X ) ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := X
% 0.72/1.08 Y := Y
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 0 ==> 0
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 subsumption: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 0.72/1.08 unorthogonal_lines( X, Y ) }.
% 0.72/1.08 parent0: (3928) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ),
% 0.72/1.08 unorthogonal_lines( X, Y ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := X
% 0.72/1.08 Y := Y
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 0 ==> 0
% 0.72/1.08 1 ==> 1
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 subsumption: (18) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 0.72/1.08 unorthogonal_lines( X, Y ), convergent_lines( Y, Z ), alpha1( X, Z ) }.
% 0.72/1.08 parent0: (3929) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.72/1.08 unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := X
% 0.72/1.08 Y := Y
% 0.72/1.08 Z := Z
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 0 ==> 0
% 0.72/1.08 1 ==> 1
% 0.72/1.08 2 ==> 3
% 0.72/1.08 3 ==> 2
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 subsumption: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 0.72/1.08 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 0.72/1.08 }.
% 0.72/1.08 parent0: (3930) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.72/1.08 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 0.72/1.08 }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := X
% 0.72/1.08 Y := Y
% 0.72/1.08 Z := Z
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 0 ==> 0
% 0.72/1.08 1 ==> 1
% 0.72/1.08 2 ==> 3
% 0.72/1.08 3 ==> 2
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 subsumption: (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 0.72/1.08 alpha1( X, Y ) }.
% 0.72/1.08 parent0: (3931) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines(
% 0.72/1.08 X, Y ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := X
% 0.72/1.08 Y := Y
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 0 ==> 1
% 0.72/1.08 1 ==> 0
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 subsumption: (21) {G0,W6,D2,L2,V2,M1} I { unorthogonal_lines( X, Y ), !
% 0.72/1.08 alpha1( X, Y ) }.
% 0.72/1.08 parent0: (3932) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), unorthogonal_lines
% 0.72/1.08 ( X, Y ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := X
% 0.72/1.08 Y := Y
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 0 ==> 1
% 0.72/1.08 1 ==> 0
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 subsumption: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 0.72/1.08 orthogonal_through_point( Y, X ), Y ) }.
% 0.72/1.08 parent0: (3934) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines(
% 0.72/1.08 orthogonal_through_point( Y, X ), Y ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := X
% 0.72/1.08 Y := Y
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 0 ==> 0
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 subsumption: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.72/1.08 orthogonal_through_point( Y, X ) ) }.
% 0.72/1.08 parent0: (3935) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.72/1.08 orthogonal_through_point( Y, X ) ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := X
% 0.72/1.08 Y := Y
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 0 ==> 0
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 subsumption: (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ),
% 0.72/1.08 unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ) }.
% 0.72/1.08 parent0: (3943) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ),
% 0.72/1.08 unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := X
% 0.72/1.08 Y := Y
% 0.72/1.08 Z := Z
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 0 ==> 1
% 0.72/1.08 1 ==> 2
% 0.72/1.08 2 ==> 0
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 subsumption: (43) {G0,W6,D2,L2,V2,M1} I { apart_point_and_line( X, Y ),
% 0.72/1.08 incident_point_and_line( X, Y ) }.
% 0.72/1.08 parent0: (3955) {G0,W6,D2,L2,V2,M2} { apart_point_and_line( X, Y ),
% 0.72/1.08 incident_point_and_line( X, Y ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := X
% 0.72/1.08 Y := Y
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 0 ==> 0
% 0.72/1.08 1 ==> 1
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 subsumption: (49) {G0,W6,D2,L2,V0,M1} I { ! incident_point_and_line( skol1
% 0.72/1.08 , skol2 ), ! incident_point_and_line( skol1, skol3 ) }.
% 0.72/1.08 parent0: (3961) {G0,W6,D2,L2,V0,M2} { ! incident_point_and_line( skol1,
% 0.72/1.08 skol2 ), ! incident_point_and_line( skol1, skol3 ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 0 ==> 0
% 0.72/1.08 1 ==> 1
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 resolution: (4116) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 0.72/1.08 distinct_lines( X, Y ) }.
% 0.72/1.08 parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.72/1.08 parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 0.72/1.08 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := X
% 0.72/1.08 end
% 0.72/1.08 substitution1:
% 0.72/1.08 X := X
% 0.72/1.08 Y := Y
% 0.72/1.08 Z := X
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 subsumption: (56) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 0.72/1.08 distinct_lines( X, Y ) }.
% 0.72/1.08 parent0: (4116) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 0.72/1.08 distinct_lines( X, Y ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := Y
% 0.72/1.08 Y := X
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 0 ==> 1
% 0.72/1.08 1 ==> 0
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 resolution: (4118) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 0.72/1.08 convergent_lines( X, Y ) }.
% 0.72/1.08 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.72/1.08 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 0.72/1.08 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := X
% 0.72/1.08 end
% 0.72/1.08 substitution1:
% 0.72/1.08 X := X
% 0.72/1.08 Y := Y
% 0.72/1.08 Z := X
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 subsumption: (67) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.72/1.08 convergent_lines( X, Y ) }.
% 0.72/1.08 parent0: (4118) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 0.72/1.08 convergent_lines( X, Y ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := Y
% 0.72/1.08 Y := X
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 0 ==> 1
% 0.72/1.08 1 ==> 0
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 resolution: (4120) {G1,W9,D2,L3,V3,M3} { convergent_lines( Y, X ),
% 0.72/1.08 convergent_lines( Z, Y ), ! convergent_lines( X, Z ) }.
% 0.72/1.08 parent0[0]: (67) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.72/1.08 convergent_lines( X, Y ) }.
% 0.72/1.08 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 0.72/1.08 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := Y
% 0.72/1.08 Y := X
% 0.72/1.08 end
% 0.72/1.08 substitution1:
% 0.72/1.08 X := X
% 0.72/1.08 Y := Z
% 0.72/1.08 Z := Y
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 subsumption: (68) {G2,W9,D2,L3,V3,M3} R(67,5) { convergent_lines( Z, X ), !
% 0.72/1.08 convergent_lines( Y, Z ), convergent_lines( X, Y ) }.
% 0.72/1.08 parent0: (4120) {G1,W9,D2,L3,V3,M3} { convergent_lines( Y, X ),
% 0.72/1.08 convergent_lines( Z, Y ), ! convergent_lines( X, Z ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := Y
% 0.72/1.08 Y := X
% 0.72/1.08 Z := Z
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 0 ==> 2
% 0.72/1.08 1 ==> 0
% 0.72/1.08 2 ==> 1
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 resolution: (4123) {G1,W5,D3,L1,V2,M1} { ! convergent_lines( X,
% 0.72/1.08 parallel_through_point( X, Y ) ) }.
% 0.72/1.08 parent0[0]: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 0.72/1.08 parallel_through_point( Y, X ), Y ) }.
% 0.72/1.08 parent1[1]: (67) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.72/1.08 convergent_lines( X, Y ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := Y
% 0.72/1.08 Y := X
% 0.72/1.08 end
% 0.72/1.08 substitution1:
% 0.72/1.08 X := parallel_through_point( X, Y )
% 0.72/1.08 Y := X
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 subsumption: (70) {G2,W5,D3,L1,V2,M1} R(67,15) { ! convergent_lines( X,
% 0.72/1.08 parallel_through_point( X, Y ) ) }.
% 0.72/1.08 parent0: (4123) {G1,W5,D3,L1,V2,M1} { ! convergent_lines( X,
% 0.72/1.08 parallel_through_point( X, Y ) ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := X
% 0.72/1.08 Y := Y
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 0 ==> 0
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 resolution: (4124) {G1,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 0.72/1.08 parallel_through_point( X, Y ) ), ! convergent_lines( X, Z ) }.
% 0.72/1.08 parent0[0]: (70) {G2,W5,D3,L1,V2,M1} R(67,15) { ! convergent_lines( X,
% 0.72/1.08 parallel_through_point( X, Y ) ) }.
% 0.72/1.08 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 0.72/1.08 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := X
% 0.72/1.08 Y := Y
% 0.72/1.08 end
% 0.72/1.08 substitution1:
% 0.72/1.08 X := X
% 0.72/1.08 Y := Z
% 0.72/1.08 Z := parallel_through_point( X, Y )
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 subsumption: (72) {G3,W8,D3,L2,V3,M2} R(70,5) { ! convergent_lines( Y, X )
% 0.72/1.08 , convergent_lines( X, parallel_through_point( Y, Z ) ) }.
% 0.72/1.08 parent0: (4124) {G1,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 0.72/1.08 parallel_through_point( X, Y ) ), ! convergent_lines( X, Z ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := Y
% 0.72/1.08 Y := Z
% 0.72/1.08 Z := X
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 0 ==> 1
% 0.72/1.08 1 ==> 0
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 resolution: (4126) {G1,W5,D3,L1,V2,M1} { convergent_lines(
% 0.72/1.08 orthogonal_through_point( X, Y ), X ) }.
% 0.72/1.08 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 0.72/1.08 orthogonal_through_point( Y, X ), Y ) }.
% 0.72/1.08 parent1[1]: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 0.72/1.08 unorthogonal_lines( X, Y ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := Y
% 0.72/1.08 Y := X
% 0.72/1.08 end
% 0.72/1.08 substitution1:
% 0.72/1.08 X := orthogonal_through_point( X, Y )
% 0.72/1.08 Y := X
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 subsumption: (108) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 0.72/1.08 orthogonal_through_point( X, Y ), X ) }.
% 0.72/1.08 parent0: (4126) {G1,W5,D3,L1,V2,M1} { convergent_lines(
% 0.72/1.08 orthogonal_through_point( X, Y ), X ) }.
% 0.72/1.08 substitution0:
% 0.72/1.08 X := X
% 0.72/1.08 Y := Y
% 0.72/1.08 end
% 0.72/1.08 permutation0:
% 0.72/1.08 0 ==> 0
% 0.72/1.08 end
% 0.72/1.08
% 0.72/1.08 resolution: (4127) {G1,W8,D3,L2,V3,M2} { convergent_lines(
% 0.72/1.09 orthogonal_through_point( X, Y ), Z ), convergent_lines( X, Z ) }.
% 0.72/1.09 parent0[2]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 0.72/1.09 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.72/1.09 parent1[0]: (108) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 0.72/1.09 orthogonal_through_point( X, Y ), X ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := orthogonal_through_point( X, Y )
% 0.72/1.09 Y := X
% 0.72/1.09 Z := Z
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (110) {G2,W8,D3,L2,V3,M2} R(108,5) { convergent_lines( X, Z )
% 0.72/1.09 , convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.72/1.09 parent0: (4127) {G1,W8,D3,L2,V3,M2} { convergent_lines(
% 0.72/1.09 orthogonal_through_point( X, Y ), Z ), convergent_lines( X, Z ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 Z := Z
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 1
% 0.72/1.09 1 ==> 0
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4128) {G1,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), !
% 0.72/1.09 distinct_lines( Y, X ) }.
% 0.72/1.09 parent0[1]: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 0.72/1.09 distinct_lines( X, Y ) }.
% 0.72/1.09 parent1[1]: (56) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 0.72/1.09 distinct_lines( X, Y ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (122) {G2,W6,D2,L2,V2,M1} R(14,56) { convergent_lines( X, Y )
% 0.72/1.09 , ! distinct_lines( Y, X ) }.
% 0.72/1.09 parent0: (4128) {G1,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), !
% 0.72/1.09 distinct_lines( Y, X ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 0
% 0.72/1.09 1 ==> 1
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4129) {G1,W12,D2,L4,V4,M4} { distinct_lines( X, Y ),
% 0.72/1.09 apart_point_and_line( Z, Y ), distinct_lines( T, X ), !
% 0.72/1.09 apart_point_and_line( Z, T ) }.
% 0.72/1.09 parent0[2]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 0.72/1.09 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.72/1.09 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 0.72/1.09 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := Z
% 0.72/1.09 Y := X
% 0.72/1.09 Z := Y
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := Z
% 0.72/1.09 Y := T
% 0.72/1.09 Z := X
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (132) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ),
% 0.72/1.09 distinct_lines( Y, T ), apart_point_and_line( Z, T ), !
% 0.72/1.09 apart_point_and_line( Z, X ) }.
% 0.72/1.09 parent0: (4129) {G1,W12,D2,L4,V4,M4} { distinct_lines( X, Y ),
% 0.72/1.09 apart_point_and_line( Z, Y ), distinct_lines( T, X ), !
% 0.72/1.09 apart_point_and_line( Z, T ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := Y
% 0.72/1.09 Y := T
% 0.72/1.09 Z := Z
% 0.72/1.09 T := X
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 1
% 0.72/1.09 1 ==> 2
% 0.72/1.09 2 ==> 0
% 0.72/1.09 3 ==> 3
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4131) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 0.72/1.09 parallel_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 0.72/1.09 parent0[0]: (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.72/1.09 parallel_through_point( Y, X ) ) }.
% 0.72/1.09 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 0.72/1.09 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Z
% 0.72/1.09 Z := parallel_through_point( Y, X )
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (142) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X,
% 0.72/1.09 parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.09 parent0: (4131) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 0.72/1.09 parallel_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := Z
% 0.72/1.09 Y := Y
% 0.72/1.09 Z := X
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 0
% 0.72/1.09 1 ==> 1
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4132) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 0.72/1.09 orthogonal_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 0.72/1.09 parent0[0]: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.72/1.09 orthogonal_through_point( Y, X ) ) }.
% 0.72/1.09 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 0.72/1.09 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Z
% 0.72/1.09 Z := orthogonal_through_point( Y, X )
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (143) {G1,W8,D3,L2,V3,M1} R(12,24) { distinct_lines( X,
% 0.72/1.09 orthogonal_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.09 parent0: (4132) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 0.72/1.09 orthogonal_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := Z
% 0.72/1.09 Y := Y
% 0.72/1.09 Z := X
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 0
% 0.72/1.09 1 ==> 1
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4134) {G1,W12,D2,L4,V3,M4} { unorthogonal_lines( X, Y ), !
% 0.72/1.09 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ), convergent_lines
% 0.72/1.09 ( Z, Y ) }.
% 0.72/1.09 parent0[1]: (21) {G0,W6,D2,L2,V2,M1} I { unorthogonal_lines( X, Y ), !
% 0.72/1.09 alpha1( X, Y ) }.
% 0.72/1.09 parent1[3]: (18) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 0.72/1.09 unorthogonal_lines( X, Y ), convergent_lines( Y, Z ), alpha1( X, Z ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Z
% 0.72/1.09 Z := Y
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (159) {G1,W12,D2,L4,V3,M2} R(18,21) { ! convergent_lines( X, Y
% 0.72/1.09 ), convergent_lines( Y, Z ), unorthogonal_lines( X, Z ), !
% 0.72/1.09 unorthogonal_lines( X, Y ) }.
% 0.72/1.09 parent0: (4134) {G1,W12,D2,L4,V3,M4} { unorthogonal_lines( X, Y ), !
% 0.72/1.09 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ), convergent_lines
% 0.72/1.09 ( Z, Y ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Z
% 0.72/1.09 Z := Y
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 2
% 0.72/1.09 1 ==> 0
% 0.72/1.09 2 ==> 3
% 0.72/1.09 3 ==> 1
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4136) {G1,W12,D2,L4,V3,M4} { convergent_lines( X, Y ), !
% 0.72/1.09 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ),
% 0.72/1.09 unorthogonal_lines( Z, Y ) }.
% 0.72/1.09 parent0[1]: (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! alpha1
% 0.72/1.09 ( X, Y ) }.
% 0.72/1.09 parent1[3]: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 0.72/1.09 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 0.72/1.09 }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Z
% 0.72/1.09 Z := Y
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (165) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y
% 0.72/1.09 ), convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 0.72/1.09 unorthogonal_lines( Y, Z ) }.
% 0.72/1.09 parent0: (4136) {G1,W12,D2,L4,V3,M4} { convergent_lines( X, Y ), !
% 0.72/1.09 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ),
% 0.72/1.09 unorthogonal_lines( Z, Y ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Z
% 0.72/1.09 Z := Y
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 1
% 0.72/1.09 1 ==> 0
% 0.72/1.09 2 ==> 2
% 0.72/1.09 3 ==> 3
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4138) {G1,W12,D2,L4,V3,M4} { unorthogonal_lines( X, Y ), !
% 0.72/1.09 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ),
% 0.72/1.09 unorthogonal_lines( Z, Y ) }.
% 0.72/1.09 parent0[1]: (21) {G0,W6,D2,L2,V2,M1} I { unorthogonal_lines( X, Y ), !
% 0.72/1.09 alpha1( X, Y ) }.
% 0.72/1.09 parent1[3]: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 0.72/1.09 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 0.72/1.09 }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Z
% 0.72/1.09 Z := Y
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (166) {G1,W12,D2,L4,V3,M3} R(19,21) { ! convergent_lines( X, Y
% 0.72/1.09 ), unorthogonal_lines( Y, Z ), unorthogonal_lines( X, Z ), !
% 0.72/1.09 unorthogonal_lines( X, Y ) }.
% 0.72/1.09 parent0: (4138) {G1,W12,D2,L4,V3,M4} { unorthogonal_lines( X, Y ), !
% 0.72/1.09 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ),
% 0.72/1.09 unorthogonal_lines( Z, Y ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Z
% 0.72/1.09 Z := Y
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 2
% 0.72/1.09 1 ==> 0
% 0.72/1.09 2 ==> 3
% 0.72/1.09 3 ==> 1
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4141) {G1,W6,D2,L2,V0,M2} { ! incident_point_and_line( skol1
% 0.72/1.09 , skol2 ), apart_point_and_line( skol1, skol3 ) }.
% 0.72/1.09 parent0[1]: (49) {G0,W6,D2,L2,V0,M1} I { ! incident_point_and_line( skol1,
% 0.72/1.09 skol2 ), ! incident_point_and_line( skol1, skol3 ) }.
% 0.72/1.09 parent1[1]: (43) {G0,W6,D2,L2,V2,M1} I { apart_point_and_line( X, Y ),
% 0.72/1.09 incident_point_and_line( X, Y ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := skol1
% 0.72/1.09 Y := skol3
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (167) {G1,W6,D2,L2,V0,M1} R(49,43) { apart_point_and_line(
% 0.72/1.09 skol1, skol3 ), ! incident_point_and_line( skol1, skol2 ) }.
% 0.72/1.09 parent0: (4141) {G1,W6,D2,L2,V0,M2} { ! incident_point_and_line( skol1,
% 0.72/1.09 skol2 ), apart_point_and_line( skol1, skol3 ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 1
% 0.72/1.09 1 ==> 0
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4142) {G1,W6,D2,L2,V0,M2} { apart_point_and_line( skol1,
% 0.72/1.09 skol3 ), apart_point_and_line( skol1, skol2 ) }.
% 0.72/1.09 parent0[1]: (167) {G1,W6,D2,L2,V0,M1} R(49,43) { apart_point_and_line(
% 0.72/1.09 skol1, skol3 ), ! incident_point_and_line( skol1, skol2 ) }.
% 0.72/1.09 parent1[1]: (43) {G0,W6,D2,L2,V2,M1} I { apart_point_and_line( X, Y ),
% 0.72/1.09 incident_point_and_line( X, Y ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := skol1
% 0.72/1.09 Y := skol2
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (168) {G2,W6,D2,L2,V0,M1} R(167,43) { apart_point_and_line(
% 0.72/1.09 skol1, skol2 ), apart_point_and_line( skol1, skol3 ) }.
% 0.72/1.09 parent0: (4142) {G1,W6,D2,L2,V0,M2} { apart_point_and_line( skol1, skol3 )
% 0.72/1.09 , apart_point_and_line( skol1, skol2 ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 1
% 0.72/1.09 1 ==> 0
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4143) {G2,W8,D3,L2,V3,M2} { convergent_lines( Y, X ),
% 0.72/1.09 convergent_lines( orthogonal_through_point( X, Z ), Y ) }.
% 0.72/1.09 parent0[0]: (67) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.72/1.09 convergent_lines( X, Y ) }.
% 0.72/1.09 parent1[0]: (110) {G2,W8,D3,L2,V3,M2} R(108,5) { convergent_lines( X, Z ),
% 0.72/1.09 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := Y
% 0.72/1.09 Y := X
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Z
% 0.72/1.09 Z := Y
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (190) {G3,W8,D3,L2,V3,M2} R(110,67) { convergent_lines( Z, X )
% 0.72/1.09 , convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.72/1.09 parent0: (4143) {G2,W8,D3,L2,V3,M2} { convergent_lines( Y, X ),
% 0.72/1.09 convergent_lines( orthogonal_through_point( X, Z ), Y ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Z
% 0.72/1.09 Z := Y
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 0
% 0.72/1.09 1 ==> 1
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4146) {G2,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 0.72/1.09 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ) }.
% 0.72/1.09 parent0[0]: (67) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.72/1.09 convergent_lines( X, Y ) }.
% 0.72/1.09 parent1[1]: (190) {G3,W8,D3,L2,V3,M2} R(110,67) { convergent_lines( Z, X )
% 0.72/1.09 , convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := Z
% 0.72/1.09 Y := orthogonal_through_point( X, Y )
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 Z := Z
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (203) {G4,W8,D3,L2,V3,M2} R(190,67) { convergent_lines( X,
% 0.72/1.09 orthogonal_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 0.72/1.09 parent0: (4146) {G2,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 0.72/1.09 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := Y
% 0.72/1.09 Y := Z
% 0.72/1.09 Z := X
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 0
% 0.72/1.09 1 ==> 1
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4147) {G1,W7,D4,L1,V3,M1} { ! convergent_lines( X,
% 0.72/1.09 parallel_through_point( parallel_through_point( X, Y ), Z ) ) }.
% 0.72/1.09 parent0[0]: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 0.72/1.09 parallel_through_point( Y, X ), Y ) }.
% 0.72/1.09 parent1[1]: (72) {G3,W8,D3,L2,V3,M2} R(70,5) { ! convergent_lines( Y, X ),
% 0.72/1.09 convergent_lines( X, parallel_through_point( Y, Z ) ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := Z
% 0.72/1.09 Y := parallel_through_point( X, Y )
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := parallel_through_point( parallel_through_point( X, Y ), Z )
% 0.72/1.09 Y := X
% 0.72/1.09 Z := Y
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (236) {G4,W7,D4,L1,V3,M1} R(72,15) { ! convergent_lines( X,
% 0.72/1.09 parallel_through_point( parallel_through_point( X, Y ), Z ) ) }.
% 0.72/1.09 parent0: (4147) {G1,W7,D4,L1,V3,M1} { ! convergent_lines( X,
% 0.72/1.09 parallel_through_point( parallel_through_point( X, Y ), Z ) ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 Z := Z
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 0
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4148) {G2,W7,D4,L1,V3,M1} { ! convergent_lines(
% 0.72/1.09 parallel_through_point( parallel_through_point( X, Y ), Z ), X ) }.
% 0.72/1.09 parent0[0]: (236) {G4,W7,D4,L1,V3,M1} R(72,15) { ! convergent_lines( X,
% 0.72/1.09 parallel_through_point( parallel_through_point( X, Y ), Z ) ) }.
% 0.72/1.09 parent1[1]: (67) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.72/1.09 convergent_lines( X, Y ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 Z := Z
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := X
% 0.72/1.09 Y := parallel_through_point( parallel_through_point( X, Y ), Z )
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (246) {G5,W7,D4,L1,V3,M1} R(236,67) { ! convergent_lines(
% 0.72/1.09 parallel_through_point( parallel_through_point( X, Y ), Z ), X ) }.
% 0.72/1.09 parent0: (4148) {G2,W7,D4,L1,V3,M1} { ! convergent_lines(
% 0.72/1.09 parallel_through_point( parallel_through_point( X, Y ), Z ), X ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 Z := Z
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 0
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4149) {G4,W9,D5,L1,V4,M1} { ! convergent_lines( X,
% 0.72/1.09 parallel_through_point( parallel_through_point( parallel_through_point( X
% 0.72/1.09 , Y ), Z ), T ) ) }.
% 0.72/1.09 parent0[0]: (246) {G5,W7,D4,L1,V3,M1} R(236,67) { ! convergent_lines(
% 0.72/1.09 parallel_through_point( parallel_through_point( X, Y ), Z ), X ) }.
% 0.72/1.09 parent1[1]: (72) {G3,W8,D3,L2,V3,M2} R(70,5) { ! convergent_lines( Y, X ),
% 0.72/1.09 convergent_lines( X, parallel_through_point( Y, Z ) ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := parallel_through_point( X, Y )
% 0.72/1.09 Y := Z
% 0.72/1.09 Z := T
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := parallel_through_point( parallel_through_point(
% 0.72/1.09 parallel_through_point( X, Y ), Z ), T )
% 0.72/1.09 Y := X
% 0.72/1.09 Z := Y
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (249) {G6,W9,D5,L1,V4,M1} R(246,72) { ! convergent_lines( X,
% 0.72/1.09 parallel_through_point( parallel_through_point( parallel_through_point( X
% 0.72/1.09 , Y ), Z ), T ) ) }.
% 0.72/1.09 parent0: (4149) {G4,W9,D5,L1,V4,M1} { ! convergent_lines( X,
% 0.72/1.09 parallel_through_point( parallel_through_point( parallel_through_point( X
% 0.72/1.09 , Y ), Z ), T ) ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 Z := Z
% 0.72/1.09 T := T
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 0
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4151) {G1,W8,D3,L2,V3,M2} { ! convergent_lines( Z, X ),
% 0.72/1.09 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.72/1.09 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 0.72/1.09 orthogonal_through_point( Y, X ), Y ) }.
% 0.72/1.09 parent1[2]: (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ),
% 0.72/1.09 unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := Y
% 0.72/1.09 Y := X
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := Z
% 0.72/1.09 Y := X
% 0.72/1.09 Z := orthogonal_through_point( X, Y )
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (257) {G1,W8,D3,L2,V3,M1} R(31,23) { ! convergent_lines( X, Y
% 0.72/1.09 ), unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 0.72/1.09 parent0: (4151) {G1,W8,D3,L2,V3,M2} { ! convergent_lines( Z, X ),
% 0.72/1.09 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := Y
% 0.72/1.09 Y := Z
% 0.72/1.09 Z := X
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 0
% 0.72/1.09 1 ==> 1
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4152) {G2,W14,D3,L4,V5,M4} { distinct_lines( X,
% 0.72/1.09 orthogonal_through_point( Y, Z ) ), distinct_lines( T, U ),
% 0.72/1.09 distinct_lines( U, X ), ! apart_point_and_line( Z, T ) }.
% 0.72/1.09 parent0[1]: (143) {G1,W8,D3,L2,V3,M1} R(12,24) { distinct_lines( X,
% 0.72/1.09 orthogonal_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.09 parent1[2]: (132) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ),
% 0.72/1.09 distinct_lines( Y, T ), apart_point_and_line( Z, T ), !
% 0.72/1.09 apart_point_and_line( Z, X ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 Z := Z
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := T
% 0.72/1.09 Y := U
% 0.72/1.09 Z := Z
% 0.72/1.09 T := X
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (2371) {G2,W14,D3,L4,V5,M1} R(132,143) { distinct_lines( X, Y
% 0.72/1.09 ), distinct_lines( Y, Z ), distinct_lines( Z, orthogonal_through_point(
% 0.72/1.09 U, T ) ), ! apart_point_and_line( T, X ) }.
% 0.72/1.09 parent0: (4152) {G2,W14,D3,L4,V5,M4} { distinct_lines( X,
% 0.72/1.09 orthogonal_through_point( Y, Z ) ), distinct_lines( T, U ),
% 0.72/1.09 distinct_lines( U, X ), ! apart_point_and_line( Z, T ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := Z
% 0.72/1.09 Y := U
% 0.72/1.09 Z := T
% 0.72/1.09 T := X
% 0.72/1.09 U := Y
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 2
% 0.72/1.09 1 ==> 0
% 0.72/1.09 2 ==> 1
% 0.72/1.09 3 ==> 3
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4157) {G2,W14,D3,L4,V5,M4} { distinct_lines( X,
% 0.72/1.09 parallel_through_point( Y, Z ) ), distinct_lines( T, U ), distinct_lines
% 0.72/1.09 ( U, X ), ! apart_point_and_line( Z, T ) }.
% 0.72/1.09 parent0[1]: (142) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X,
% 0.72/1.09 parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.09 parent1[2]: (132) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ),
% 0.72/1.09 distinct_lines( Y, T ), apart_point_and_line( Z, T ), !
% 0.72/1.09 apart_point_and_line( Z, X ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 Z := Z
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := T
% 0.72/1.09 Y := U
% 0.72/1.09 Z := Z
% 0.72/1.09 T := X
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (2372) {G2,W14,D3,L4,V5,M1} R(132,142) { distinct_lines( X, Y
% 0.72/1.09 ), distinct_lines( Y, Z ), distinct_lines( Z, parallel_through_point( U
% 0.72/1.09 , T ) ), ! apart_point_and_line( T, X ) }.
% 0.72/1.09 parent0: (4157) {G2,W14,D3,L4,V5,M4} { distinct_lines( X,
% 0.72/1.09 parallel_through_point( Y, Z ) ), distinct_lines( T, U ), distinct_lines
% 0.72/1.09 ( U, X ), ! apart_point_and_line( Z, T ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := Z
% 0.72/1.09 Y := U
% 0.72/1.09 Z := T
% 0.72/1.09 T := X
% 0.72/1.09 U := Y
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 2
% 0.72/1.09 1 ==> 0
% 0.72/1.09 2 ==> 1
% 0.72/1.09 3 ==> 3
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 factor: (4163) {G2,W13,D3,L3,V3,M3} { distinct_lines( X,
% 0.72/1.09 parallel_through_point( Y, Z ) ), distinct_lines( parallel_through_point
% 0.72/1.09 ( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.09 parent0[0, 2]: (2372) {G2,W14,D3,L4,V5,M1} R(132,142) { distinct_lines( X,
% 0.72/1.09 Y ), distinct_lines( Y, Z ), distinct_lines( Z, parallel_through_point( U
% 0.72/1.09 , T ) ), ! apart_point_and_line( T, X ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := parallel_through_point( Y, Z )
% 0.72/1.09 Z := X
% 0.72/1.09 T := Z
% 0.72/1.09 U := Y
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4169) {G2,W13,D3,L3,V3,M3} { distinct_lines(
% 0.72/1.09 parallel_through_point( Y, Z ), X ), distinct_lines(
% 0.72/1.09 parallel_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.09 parent0[0]: (56) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 0.72/1.09 distinct_lines( X, Y ) }.
% 0.72/1.09 parent1[0]: (4163) {G2,W13,D3,L3,V3,M3} { distinct_lines( X,
% 0.72/1.09 parallel_through_point( Y, Z ) ), distinct_lines( parallel_through_point
% 0.72/1.09 ( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := parallel_through_point( Y, Z )
% 0.72/1.09 Y := X
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 Z := Z
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 factor: (4171) {G2,W8,D3,L2,V3,M2} { distinct_lines(
% 0.72/1.09 parallel_through_point( X, Y ), Z ), ! apart_point_and_line( Y, Z ) }.
% 0.72/1.09 parent0[0, 1]: (4169) {G2,W13,D3,L3,V3,M3} { distinct_lines(
% 0.72/1.09 parallel_through_point( Y, Z ), X ), distinct_lines(
% 0.72/1.09 parallel_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := Z
% 0.72/1.09 Y := X
% 0.72/1.09 Z := Y
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (2380) {G3,W8,D3,L2,V3,M1} F(2372);r(56) { distinct_lines(
% 0.72/1.09 parallel_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.09 parent0: (4171) {G2,W8,D3,L2,V3,M2} { distinct_lines(
% 0.72/1.09 parallel_through_point( X, Y ), Z ), ! apart_point_and_line( Y, Z ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := Y
% 0.72/1.09 Y := Z
% 0.72/1.09 Z := X
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 0
% 0.72/1.09 1 ==> 1
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 factor: (4174) {G2,W13,D3,L3,V3,M3} { distinct_lines( X,
% 0.72/1.09 orthogonal_through_point( Y, Z ) ), distinct_lines(
% 0.72/1.09 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.09 parent0[0, 2]: (2371) {G2,W14,D3,L4,V5,M1} R(132,143) { distinct_lines( X,
% 0.72/1.09 Y ), distinct_lines( Y, Z ), distinct_lines( Z, orthogonal_through_point
% 0.72/1.09 ( U, T ) ), ! apart_point_and_line( T, X ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := orthogonal_through_point( Y, Z )
% 0.72/1.09 Z := X
% 0.72/1.09 T := Z
% 0.72/1.09 U := Y
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4180) {G2,W13,D3,L3,V3,M3} { distinct_lines(
% 0.72/1.09 orthogonal_through_point( Y, Z ), X ), distinct_lines(
% 0.72/1.09 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.09 parent0[0]: (56) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 0.72/1.09 distinct_lines( X, Y ) }.
% 0.72/1.09 parent1[0]: (4174) {G2,W13,D3,L3,V3,M3} { distinct_lines( X,
% 0.72/1.09 orthogonal_through_point( Y, Z ) ), distinct_lines(
% 0.72/1.09 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := orthogonal_through_point( Y, Z )
% 0.72/1.09 Y := X
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 Z := Z
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 factor: (4182) {G2,W8,D3,L2,V3,M2} { distinct_lines(
% 0.72/1.09 orthogonal_through_point( X, Y ), Z ), ! apart_point_and_line( Y, Z ) }.
% 0.72/1.09 parent0[0, 1]: (4180) {G2,W13,D3,L3,V3,M3} { distinct_lines(
% 0.72/1.09 orthogonal_through_point( Y, Z ), X ), distinct_lines(
% 0.72/1.09 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := Z
% 0.72/1.09 Y := X
% 0.72/1.09 Z := Y
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (2381) {G3,W8,D3,L2,V3,M1} F(2371);r(56) { distinct_lines(
% 0.72/1.09 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.09 parent0: (4182) {G2,W8,D3,L2,V3,M2} { distinct_lines(
% 0.72/1.09 orthogonal_through_point( X, Y ), Z ), ! apart_point_and_line( Y, Z ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := Y
% 0.72/1.09 Y := Z
% 0.72/1.09 Z := X
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 0
% 0.72/1.09 1 ==> 1
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4185) {G3,W8,D3,L2,V1,M2} { distinct_lines(
% 0.72/1.09 orthogonal_through_point( X, skol1 ), skol3 ), apart_point_and_line(
% 0.72/1.09 skol1, skol2 ) }.
% 0.72/1.09 parent0[1]: (2381) {G3,W8,D3,L2,V3,M1} F(2371);r(56) { distinct_lines(
% 0.72/1.09 orthogonal_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.09 parent1[1]: (168) {G2,W6,D2,L2,V0,M1} R(167,43) { apart_point_and_line(
% 0.72/1.09 skol1, skol2 ), apart_point_and_line( skol1, skol3 ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := skol3
% 0.72/1.09 Y := X
% 0.72/1.09 Z := skol1
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (2402) {G4,W8,D3,L2,V1,M1} R(2381,168) { distinct_lines(
% 0.72/1.09 orthogonal_through_point( X, skol1 ), skol3 ), apart_point_and_line(
% 0.72/1.09 skol1, skol2 ) }.
% 0.72/1.09 parent0: (4185) {G3,W8,D3,L2,V1,M2} { distinct_lines(
% 0.72/1.09 orthogonal_through_point( X, skol1 ), skol3 ), apart_point_and_line(
% 0.72/1.09 skol1, skol2 ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 0
% 0.72/1.09 1 ==> 1
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4186) {G4,W10,D3,L2,V2,M2} { distinct_lines(
% 0.72/1.09 parallel_through_point( X, skol1 ), skol2 ), distinct_lines(
% 0.72/1.09 orthogonal_through_point( Y, skol1 ), skol3 ) }.
% 0.72/1.09 parent0[1]: (2380) {G3,W8,D3,L2,V3,M1} F(2372);r(56) { distinct_lines(
% 0.72/1.09 parallel_through_point( Y, Z ), X ), ! apart_point_and_line( Z, X ) }.
% 0.72/1.09 parent1[1]: (2402) {G4,W8,D3,L2,V1,M1} R(2381,168) { distinct_lines(
% 0.72/1.09 orthogonal_through_point( X, skol1 ), skol3 ), apart_point_and_line(
% 0.72/1.09 skol1, skol2 ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := skol2
% 0.72/1.09 Y := X
% 0.72/1.09 Z := skol1
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := Y
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (2437) {G5,W10,D3,L2,V2,M1} R(2402,2380) { distinct_lines(
% 0.72/1.09 parallel_through_point( Y, skol1 ), skol2 ), distinct_lines(
% 0.72/1.09 orthogonal_through_point( X, skol1 ), skol3 ) }.
% 0.72/1.09 parent0: (4186) {G4,W10,D3,L2,V2,M2} { distinct_lines(
% 0.72/1.09 parallel_through_point( X, skol1 ), skol2 ), distinct_lines(
% 0.72/1.09 orthogonal_through_point( Y, skol1 ), skol3 ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := Y
% 0.72/1.09 Y := X
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 0
% 0.72/1.09 1 ==> 1
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4188) {G3,W10,D3,L2,V2,M2} { convergent_lines( skol3,
% 0.72/1.09 orthogonal_through_point( X, skol1 ) ), distinct_lines(
% 0.72/1.09 parallel_through_point( Y, skol1 ), skol2 ) }.
% 0.72/1.09 parent0[1]: (122) {G2,W6,D2,L2,V2,M1} R(14,56) { convergent_lines( X, Y ),
% 0.72/1.09 ! distinct_lines( Y, X ) }.
% 0.72/1.09 parent1[1]: (2437) {G5,W10,D3,L2,V2,M1} R(2402,2380) { distinct_lines(
% 0.72/1.09 parallel_through_point( Y, skol1 ), skol2 ), distinct_lines(
% 0.72/1.09 orthogonal_through_point( X, skol1 ), skol3 ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := skol3
% 0.72/1.09 Y := orthogonal_through_point( X, skol1 )
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (2840) {G6,W10,D3,L2,V2,M1} R(2437,122) { convergent_lines(
% 0.72/1.09 skol3, orthogonal_through_point( Y, skol1 ) ), distinct_lines(
% 0.72/1.09 parallel_through_point( X, skol1 ), skol2 ) }.
% 0.72/1.09 parent0: (4188) {G3,W10,D3,L2,V2,M2} { convergent_lines( skol3,
% 0.72/1.09 orthogonal_through_point( X, skol1 ) ), distinct_lines(
% 0.72/1.09 parallel_through_point( Y, skol1 ), skol2 ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := Y
% 0.72/1.09 Y := X
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 0
% 0.72/1.09 1 ==> 1
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4189) {G3,W10,D3,L2,V2,M2} { convergent_lines( skol2,
% 0.72/1.09 parallel_through_point( X, skol1 ) ), convergent_lines( skol3,
% 0.72/1.09 orthogonal_through_point( Y, skol1 ) ) }.
% 0.72/1.09 parent0[1]: (122) {G2,W6,D2,L2,V2,M1} R(14,56) { convergent_lines( X, Y ),
% 0.72/1.09 ! distinct_lines( Y, X ) }.
% 0.72/1.09 parent1[1]: (2840) {G6,W10,D3,L2,V2,M1} R(2437,122) { convergent_lines(
% 0.72/1.09 skol3, orthogonal_through_point( Y, skol1 ) ), distinct_lines(
% 0.72/1.09 parallel_through_point( X, skol1 ), skol2 ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := skol2
% 0.72/1.09 Y := parallel_through_point( X, skol1 )
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (2858) {G7,W10,D3,L2,V2,M1} R(2840,122) { convergent_lines(
% 0.72/1.09 skol3, orthogonal_through_point( X, skol1 ) ), convergent_lines( skol2,
% 0.72/1.09 parallel_through_point( Y, skol1 ) ) }.
% 0.72/1.09 parent0: (4189) {G3,W10,D3,L2,V2,M2} { convergent_lines( skol2,
% 0.72/1.09 parallel_through_point( X, skol1 ) ), convergent_lines( skol3,
% 0.72/1.09 orthogonal_through_point( Y, skol1 ) ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := Y
% 0.72/1.09 Y := X
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 1
% 0.72/1.09 1 ==> 0
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4190) {G7,W5,D3,L1,V1,M1} { convergent_lines( skol3,
% 0.72/1.09 orthogonal_through_point( Z, skol1 ) ) }.
% 0.72/1.09 parent0[0]: (249) {G6,W9,D5,L1,V4,M1} R(246,72) { ! convergent_lines( X,
% 0.72/1.09 parallel_through_point( parallel_through_point( parallel_through_point( X
% 0.72/1.09 , Y ), Z ), T ) ) }.
% 0.72/1.09 parent1[1]: (2858) {G7,W10,D3,L2,V2,M1} R(2840,122) { convergent_lines(
% 0.72/1.09 skol3, orthogonal_through_point( X, skol1 ) ), convergent_lines( skol2,
% 0.72/1.09 parallel_through_point( Y, skol1 ) ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := skol2
% 0.72/1.09 Y := X
% 0.72/1.09 Z := Y
% 0.72/1.09 T := skol1
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := Z
% 0.72/1.09 Y := parallel_through_point( parallel_through_point( skol2, X ), Y )
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (2868) {G8,W5,D3,L1,V1,M1} R(2858,249) { convergent_lines(
% 0.72/1.09 skol3, orthogonal_through_point( X, skol1 ) ) }.
% 0.72/1.09 parent0: (4190) {G7,W5,D3,L1,V1,M1} { convergent_lines( skol3,
% 0.72/1.09 orthogonal_through_point( Z, skol1 ) ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := Y
% 0.72/1.09 Y := Z
% 0.72/1.09 Z := X
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 0
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4191) {G3,W8,D3,L2,V2,M2} { convergent_lines(
% 0.72/1.09 orthogonal_through_point( X, skol1 ), Y ), convergent_lines( Y, skol3 )
% 0.72/1.09 }.
% 0.72/1.09 parent0[1]: (68) {G2,W9,D2,L3,V3,M3} R(67,5) { convergent_lines( Z, X ), !
% 0.72/1.09 convergent_lines( Y, Z ), convergent_lines( X, Y ) }.
% 0.72/1.09 parent1[0]: (2868) {G8,W5,D3,L1,V1,M1} R(2858,249) { convergent_lines(
% 0.72/1.09 skol3, orthogonal_through_point( X, skol1 ) ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := Y
% 0.72/1.09 Y := skol3
% 0.72/1.09 Z := orthogonal_through_point( X, skol1 )
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := X
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (2873) {G9,W8,D3,L2,V2,M2} R(2868,68) { convergent_lines( Y,
% 0.72/1.09 skol3 ), convergent_lines( orthogonal_through_point( X, skol1 ), Y ) }.
% 0.72/1.09 parent0: (4191) {G3,W8,D3,L2,V2,M2} { convergent_lines(
% 0.72/1.09 orthogonal_through_point( X, skol1 ), Y ), convergent_lines( Y, skol3 )
% 0.72/1.09 }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 1
% 0.72/1.09 1 ==> 0
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4192) {G1,W13,D3,L3,V3,M3} { ! convergent_lines(
% 0.72/1.09 orthogonal_through_point( X, Y ), Z ), convergent_lines( Z, X ), !
% 0.72/1.09 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.72/1.09 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 0.72/1.09 orthogonal_through_point( Y, X ), Y ) }.
% 0.72/1.09 parent1[2]: (159) {G1,W12,D2,L4,V3,M2} R(18,21) { ! convergent_lines( X, Y
% 0.72/1.09 ), convergent_lines( Y, Z ), unorthogonal_lines( X, Z ), !
% 0.72/1.09 unorthogonal_lines( X, Y ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := Y
% 0.72/1.09 Y := X
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := orthogonal_through_point( X, Y )
% 0.72/1.09 Y := Z
% 0.72/1.09 Z := X
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4194) {G2,W11,D3,L3,V3,M3} { convergent_lines( Z, X ), !
% 0.72/1.09 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ),
% 0.72/1.09 convergent_lines( Z, X ) }.
% 0.72/1.09 parent0[0]: (4192) {G1,W13,D3,L3,V3,M3} { ! convergent_lines(
% 0.72/1.09 orthogonal_through_point( X, Y ), Z ), convergent_lines( Z, X ), !
% 0.72/1.09 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.72/1.09 parent1[1]: (190) {G3,W8,D3,L2,V3,M2} R(110,67) { convergent_lines( Z, X )
% 0.72/1.09 , convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 Z := Z
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 Z := Z
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 factor: (4195) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 0.72/1.09 unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 0.72/1.09 parent0[0, 2]: (4194) {G2,W11,D3,L3,V3,M3} { convergent_lines( Z, X ), !
% 0.72/1.09 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ),
% 0.72/1.09 convergent_lines( Z, X ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := Y
% 0.72/1.09 Y := Z
% 0.72/1.09 Z := X
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (3021) {G4,W8,D3,L2,V3,M1} R(159,23);r(190) { convergent_lines
% 0.72/1.09 ( Z, X ), ! unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.72/1.09 parent0: (4195) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 0.72/1.09 unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := Z
% 0.72/1.09 Y := X
% 0.72/1.09 Z := Y
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 0
% 0.72/1.09 1 ==> 1
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4196) {G1,W13,D3,L3,V3,M3} { ! convergent_lines( Z,
% 0.72/1.09 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ), !
% 0.72/1.09 unorthogonal_lines( Z, orthogonal_through_point( X, Y ) ) }.
% 0.72/1.09 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 0.72/1.09 orthogonal_through_point( Y, X ), Y ) }.
% 0.72/1.09 parent1[3]: (165) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y
% 0.72/1.09 ), convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 0.72/1.09 unorthogonal_lines( Y, Z ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := Y
% 0.72/1.09 Y := X
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := Z
% 0.72/1.09 Y := orthogonal_through_point( X, Y )
% 0.72/1.09 Z := X
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4197) {G2,W11,D3,L3,V3,M3} { convergent_lines( X, Y ), !
% 0.72/1.09 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ),
% 0.72/1.09 convergent_lines( X, Y ) }.
% 0.72/1.09 parent0[0]: (4196) {G1,W13,D3,L3,V3,M3} { ! convergent_lines( Z,
% 0.72/1.09 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ), !
% 0.72/1.09 unorthogonal_lines( Z, orthogonal_through_point( X, Y ) ) }.
% 0.72/1.09 parent1[0]: (203) {G4,W8,D3,L2,V3,M2} R(190,67) { convergent_lines( X,
% 0.72/1.09 orthogonal_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := Y
% 0.72/1.09 Y := Z
% 0.72/1.09 Z := X
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 Z := Z
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 factor: (4198) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 0.72/1.09 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 0.72/1.09 parent0[0, 2]: (4197) {G2,W11,D3,L3,V3,M3} { convergent_lines( X, Y ), !
% 0.72/1.09 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ),
% 0.72/1.09 convergent_lines( X, Y ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 Z := Z
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (3044) {G5,W8,D3,L2,V3,M1} R(165,23);r(203) { convergent_lines
% 0.72/1.09 ( X, Y ), ! unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 0.72/1.09 parent0: (4198) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 0.72/1.09 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 Z := Z
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 0
% 0.72/1.09 1 ==> 1
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4199) {G2,W10,D3,L2,V4,M2} { convergent_lines(
% 0.72/1.09 orthogonal_through_point( X, Y ), Z ), ! convergent_lines(
% 0.72/1.09 orthogonal_through_point( Z, T ), X ) }.
% 0.72/1.09 parent0[1]: (3044) {G5,W8,D3,L2,V3,M1} R(165,23);r(203) { convergent_lines
% 0.72/1.09 ( X, Y ), ! unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 0.72/1.09 parent1[1]: (257) {G1,W8,D3,L2,V3,M1} R(31,23) { ! convergent_lines( X, Y )
% 0.72/1.09 , unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := orthogonal_through_point( X, Y )
% 0.72/1.09 Y := Z
% 0.72/1.09 Z := T
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := orthogonal_through_point( Z, T )
% 0.72/1.09 Y := X
% 0.72/1.09 Z := Y
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (3051) {G6,W10,D3,L2,V4,M2} R(3044,257) { ! convergent_lines(
% 0.72/1.09 orthogonal_through_point( Z, T ), X ), convergent_lines(
% 0.72/1.09 orthogonal_through_point( X, Y ), Z ) }.
% 0.72/1.09 parent0: (4199) {G2,W10,D3,L2,V4,M2} { convergent_lines(
% 0.72/1.09 orthogonal_through_point( X, Y ), Z ), ! convergent_lines(
% 0.72/1.09 orthogonal_through_point( Z, T ), X ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 Z := Z
% 0.72/1.09 T := T
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 1
% 0.72/1.09 1 ==> 0
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4200) {G1,W15,D2,L5,V4,M5} { ! convergent_lines( X, Y ),
% 0.72/1.09 unorthogonal_lines( Y, Z ), unorthogonal_lines( X, Z ), !
% 0.72/1.09 convergent_lines( Y, T ), unorthogonal_lines( X, T ) }.
% 0.72/1.09 parent0[3]: (166) {G1,W12,D2,L4,V3,M3} R(19,21) { ! convergent_lines( X, Y
% 0.72/1.09 ), unorthogonal_lines( Y, Z ), unorthogonal_lines( X, Z ), !
% 0.72/1.09 unorthogonal_lines( X, Y ) }.
% 0.72/1.09 parent1[1]: (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ),
% 0.72/1.09 unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 Z := Z
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := Y
% 0.72/1.09 Y := T
% 0.72/1.09 Z := X
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (3068) {G2,W15,D2,L5,V4,M3} R(166,31) { ! convergent_lines( X
% 0.72/1.09 , Y ), ! convergent_lines( Y, T ), unorthogonal_lines( Y, Z ),
% 0.72/1.09 unorthogonal_lines( X, T ), unorthogonal_lines( X, Z ) }.
% 0.72/1.09 parent0: (4200) {G1,W15,D2,L5,V4,M5} { ! convergent_lines( X, Y ),
% 0.72/1.09 unorthogonal_lines( Y, Z ), unorthogonal_lines( X, Z ), !
% 0.72/1.09 convergent_lines( Y, T ), unorthogonal_lines( X, T ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 Z := Z
% 0.72/1.09 T := T
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 0
% 0.72/1.09 1 ==> 2
% 0.72/1.09 2 ==> 4
% 0.72/1.09 3 ==> 1
% 0.72/1.09 4 ==> 3
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 factor: (4215) {G2,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.72/1.09 convergent_lines( Y, Z ), unorthogonal_lines( Y, Z ), unorthogonal_lines
% 0.72/1.09 ( X, Z ) }.
% 0.72/1.09 parent0[3, 4]: (3068) {G2,W15,D2,L5,V4,M3} R(166,31) { ! convergent_lines(
% 0.72/1.09 X, Y ), ! convergent_lines( Y, T ), unorthogonal_lines( Y, Z ),
% 0.72/1.09 unorthogonal_lines( X, T ), unorthogonal_lines( X, Z ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 Z := Z
% 0.72/1.09 T := Z
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4239) {G1,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ),
% 0.72/1.09 unorthogonal_lines( Y, Z ), unorthogonal_lines( X, Z ),
% 0.72/1.09 unorthogonal_lines( Y, Z ) }.
% 0.72/1.09 parent0[1]: (4215) {G2,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.72/1.09 convergent_lines( Y, Z ), unorthogonal_lines( Y, Z ), unorthogonal_lines
% 0.72/1.09 ( X, Z ) }.
% 0.72/1.09 parent1[0]: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 0.72/1.09 unorthogonal_lines( X, Y ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 Z := Z
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := Y
% 0.72/1.09 Y := Z
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 factor: (4243) {G1,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 0.72/1.09 unorthogonal_lines( Y, Z ), unorthogonal_lines( X, Z ) }.
% 0.72/1.09 parent0[1, 3]: (4239) {G1,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ),
% 0.72/1.09 unorthogonal_lines( Y, Z ), unorthogonal_lines( X, Z ),
% 0.72/1.09 unorthogonal_lines( Y, Z ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 Z := Z
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (3079) {G3,W9,D2,L3,V3,M2} F(3068);r(17) { ! convergent_lines
% 0.72/1.09 ( X, Y ), unorthogonal_lines( X, Z ), unorthogonal_lines( Y, Z ) }.
% 0.72/1.09 parent0: (4243) {G1,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 0.72/1.09 unorthogonal_lines( Y, Z ), unorthogonal_lines( X, Z ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 Z := Z
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 0
% 0.72/1.09 1 ==> 2
% 0.72/1.09 2 ==> 1
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4245) {G1,W8,D3,L2,V3,M2} { ! convergent_lines(
% 0.72/1.09 orthogonal_through_point( X, Y ), Z ), unorthogonal_lines( Z, X ) }.
% 0.72/1.09 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 0.72/1.09 orthogonal_through_point( Y, X ), Y ) }.
% 0.72/1.09 parent1[1]: (3079) {G3,W9,D2,L3,V3,M2} F(3068);r(17) { ! convergent_lines(
% 0.72/1.09 X, Y ), unorthogonal_lines( X, Z ), unorthogonal_lines( Y, Z ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := Y
% 0.72/1.09 Y := X
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := orthogonal_through_point( X, Y )
% 0.72/1.09 Y := Z
% 0.72/1.09 Z := X
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (3092) {G4,W8,D3,L2,V3,M1} R(3079,23) { ! convergent_lines(
% 0.72/1.09 orthogonal_through_point( X, Y ), Z ), unorthogonal_lines( Z, X ) }.
% 0.72/1.09 parent0: (4245) {G1,W8,D3,L2,V3,M2} { ! convergent_lines(
% 0.72/1.09 orthogonal_through_point( X, Y ), Z ), unorthogonal_lines( Z, X ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 Z := Z
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 0
% 0.72/1.09 1 ==> 1
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4248) {G1,W8,D3,L2,V3,M2} { ! convergent_lines( Z,
% 0.72/1.09 orthogonal_through_point( X, Y ) ), unorthogonal_lines( Z, X ) }.
% 0.72/1.09 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 0.72/1.09 orthogonal_through_point( Y, X ), Y ) }.
% 0.72/1.09 parent1[2]: (3079) {G3,W9,D2,L3,V3,M2} F(3068);r(17) { ! convergent_lines(
% 0.72/1.09 X, Y ), unorthogonal_lines( X, Z ), unorthogonal_lines( Y, Z ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := Y
% 0.72/1.09 Y := X
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := Z
% 0.72/1.09 Y := orthogonal_through_point( X, Y )
% 0.72/1.09 Z := X
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (3093) {G4,W8,D3,L2,V3,M1} R(3079,23) { ! convergent_lines( X
% 0.72/1.09 , orthogonal_through_point( Y, Z ) ), unorthogonal_lines( X, Y ) }.
% 0.72/1.09 parent0: (4248) {G1,W8,D3,L2,V3,M2} { ! convergent_lines( Z,
% 0.72/1.09 orthogonal_through_point( X, Y ) ), unorthogonal_lines( Z, X ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := Y
% 0.72/1.09 Y := Z
% 0.72/1.09 Z := X
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 0
% 0.72/1.09 1 ==> 1
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4249) {G1,W7,D3,L1,V3,M1} { ! convergent_lines(
% 0.72/1.09 orthogonal_through_point( X, Z ), orthogonal_through_point( X, Y ) ) }.
% 0.72/1.09 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 0.72/1.09 orthogonal_through_point( Y, X ), Y ) }.
% 0.72/1.09 parent1[1]: (3092) {G4,W8,D3,L2,V3,M1} R(3079,23) { ! convergent_lines(
% 0.72/1.09 orthogonal_through_point( X, Y ), Z ), unorthogonal_lines( Z, X ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := Y
% 0.72/1.09 Y := X
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Z
% 0.72/1.09 Z := orthogonal_through_point( X, Y )
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (3138) {G5,W7,D3,L1,V3,M1} R(3092,23) { ! convergent_lines(
% 0.72/1.09 orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ) }.
% 0.72/1.09 parent0: (4249) {G1,W7,D3,L1,V3,M1} { ! convergent_lines(
% 0.72/1.09 orthogonal_through_point( X, Z ), orthogonal_through_point( X, Y ) ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Z
% 0.72/1.09 Z := Y
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 0
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4250) {G6,W5,D3,L1,V2,M1} { convergent_lines(
% 0.72/1.09 orthogonal_through_point( X, Y ), skol3 ) }.
% 0.72/1.09 parent0[0]: (3138) {G5,W7,D3,L1,V3,M1} R(3092,23) { ! convergent_lines(
% 0.72/1.09 orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ) }.
% 0.72/1.09 parent1[1]: (2873) {G9,W8,D3,L2,V2,M2} R(2868,68) { convergent_lines( Y,
% 0.72/1.09 skol3 ), convergent_lines( orthogonal_through_point( X, skol1 ), Y ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := skol1
% 0.72/1.09 Z := Y
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := X
% 0.72/1.09 Y := orthogonal_through_point( X, Y )
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (3140) {G10,W5,D3,L1,V2,M1} R(3138,2873) { convergent_lines(
% 0.72/1.09 orthogonal_through_point( X, Y ), skol3 ) }.
% 0.72/1.09 parent0: (4250) {G6,W5,D3,L1,V2,M1} { convergent_lines(
% 0.72/1.09 orthogonal_through_point( X, Y ), skol3 ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 0
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4252) {G5,W10,D3,L2,V4,M2} { convergent_lines( X, Y ), !
% 0.72/1.09 convergent_lines( orthogonal_through_point( Y, Z ),
% 0.72/1.09 orthogonal_through_point( X, T ) ) }.
% 0.72/1.09 parent0[1]: (3021) {G4,W8,D3,L2,V3,M1} R(159,23);r(190) { convergent_lines
% 0.72/1.09 ( Z, X ), ! unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.72/1.09 parent1[1]: (3093) {G4,W8,D3,L2,V3,M1} R(3079,23) { ! convergent_lines( X,
% 0.72/1.09 orthogonal_through_point( Y, Z ) ), unorthogonal_lines( X, Y ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := Y
% 0.72/1.09 Y := Z
% 0.72/1.09 Z := X
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := orthogonal_through_point( Y, Z )
% 0.72/1.09 Y := X
% 0.72/1.09 Z := T
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (3353) {G5,W10,D3,L2,V4,M2} R(3093,3021) { convergent_lines( Z
% 0.72/1.09 , X ), ! convergent_lines( orthogonal_through_point( X, Y ),
% 0.72/1.09 orthogonal_through_point( Z, T ) ) }.
% 0.72/1.09 parent0: (4252) {G5,W10,D3,L2,V4,M2} { convergent_lines( X, Y ), !
% 0.72/1.09 convergent_lines( orthogonal_through_point( Y, Z ),
% 0.72/1.09 orthogonal_through_point( X, T ) ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := Z
% 0.72/1.09 Y := X
% 0.72/1.09 Z := Y
% 0.72/1.09 T := T
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 0
% 0.72/1.09 1 ==> 1
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4253) {G1,W9,D4,L1,V4,M1} { ! convergent_lines(
% 0.72/1.09 orthogonal_through_point( X, Z ), orthogonal_through_point(
% 0.72/1.09 parallel_through_point( X, Y ), T ) ) }.
% 0.72/1.09 parent0[0]: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 0.72/1.09 parallel_through_point( Y, X ), Y ) }.
% 0.72/1.09 parent1[0]: (3353) {G5,W10,D3,L2,V4,M2} R(3093,3021) { convergent_lines( Z
% 0.72/1.09 , X ), ! convergent_lines( orthogonal_through_point( X, Y ),
% 0.72/1.09 orthogonal_through_point( Z, T ) ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := Y
% 0.72/1.09 Y := X
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Z
% 0.72/1.09 Z := parallel_through_point( X, Y )
% 0.72/1.09 T := T
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (3499) {G6,W9,D4,L1,V4,M1} R(3353,15) { ! convergent_lines(
% 0.72/1.09 orthogonal_through_point( X, Y ), orthogonal_through_point(
% 0.72/1.09 parallel_through_point( X, Z ), T ) ) }.
% 0.72/1.09 parent0: (4253) {G1,W9,D4,L1,V4,M1} { ! convergent_lines(
% 0.72/1.09 orthogonal_through_point( X, Z ), orthogonal_through_point(
% 0.72/1.09 parallel_through_point( X, Y ), T ) ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Z
% 0.72/1.09 Z := Y
% 0.72/1.09 T := T
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 0
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4254) {G7,W5,D3,L1,V2,M1} { convergent_lines(
% 0.72/1.09 orthogonal_through_point( skol3, Z ), X ) }.
% 0.72/1.09 parent0[0]: (3051) {G6,W10,D3,L2,V4,M2} R(3044,257) { ! convergent_lines(
% 0.72/1.09 orthogonal_through_point( Z, T ), X ), convergent_lines(
% 0.72/1.09 orthogonal_through_point( X, Y ), Z ) }.
% 0.72/1.09 parent1[0]: (3140) {G10,W5,D3,L1,V2,M1} R(3138,2873) { convergent_lines(
% 0.72/1.09 orthogonal_through_point( X, Y ), skol3 ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := skol3
% 0.72/1.09 Y := Z
% 0.72/1.09 Z := X
% 0.72/1.09 T := Y
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := X
% 0.72/1.09 Y := Y
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (3849) {G11,W5,D3,L1,V2,M1} R(3051,3140) { convergent_lines(
% 0.72/1.09 orthogonal_through_point( skol3, X ), Y ) }.
% 0.72/1.09 parent0: (4254) {G7,W5,D3,L1,V2,M1} { convergent_lines(
% 0.72/1.09 orthogonal_through_point( skol3, Z ), X ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := Y
% 0.72/1.09 Y := Z
% 0.72/1.09 Z := X
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 0 ==> 0
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 resolution: (4255) {G7,W0,D0,L0,V0,M0} { }.
% 0.72/1.09 parent0[0]: (3499) {G6,W9,D4,L1,V4,M1} R(3353,15) { ! convergent_lines(
% 0.72/1.09 orthogonal_through_point( X, Y ), orthogonal_through_point(
% 0.72/1.09 parallel_through_point( X, Z ), T ) ) }.
% 0.72/1.09 parent1[0]: (3849) {G11,W5,D3,L1,V2,M1} R(3051,3140) { convergent_lines(
% 0.72/1.09 orthogonal_through_point( skol3, X ), Y ) }.
% 0.72/1.09 substitution0:
% 0.72/1.09 X := skol3
% 0.72/1.09 Y := X
% 0.72/1.09 Z := Y
% 0.72/1.09 T := Z
% 0.72/1.09 end
% 0.72/1.09 substitution1:
% 0.72/1.09 X := X
% 0.72/1.09 Y := orthogonal_through_point( parallel_through_point( skol3, Y ), Z )
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 subsumption: (3908) {G12,W0,D0,L0,V0,M0} R(3849,3499) { }.
% 0.72/1.09 parent0: (4255) {G7,W0,D0,L0,V0,M0} { }.
% 0.72/1.09 substitution0:
% 0.72/1.09 end
% 0.72/1.09 permutation0:
% 0.72/1.09 end
% 0.72/1.09
% 0.72/1.09 Proof check complete!
% 0.72/1.09
% 0.72/1.09 Memory use:
% 0.72/1.09
% 0.72/1.09 space for terms: 51795
% 0.72/1.09 space for clauses: 153478
% 0.72/1.09
% 0.72/1.09
% 0.72/1.09 clauses generated: 20591
% 0.72/1.09 clauses kept: 3909
% 0.72/1.09 clauses selected: 491
% 0.72/1.09 clauses deleted: 15
% 0.72/1.09 clauses inuse deleted: 8
% 0.72/1.09
% 0.72/1.09 subsentry: 276461
% 0.72/1.09 literals s-matched: 113394
% 0.72/1.09 literals matched: 113138
% 0.72/1.09 full subsumption: 69414
% 0.72/1.09
% 0.72/1.09 checksum: 649878104
% 0.72/1.09
% 0.72/1.09
% 0.72/1.09 Bliksem ended
%------------------------------------------------------------------------------