%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO223+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 02:52:59 EDT 2022
% Result : Theorem 0.76s 1.16s
% Output : Refutation 0.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : GEO223+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.10 % Command : bliksem %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % DateTime : Sat Jun 18 18:32:47 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.76/1.16 *** allocated 10000 integers for termspace/termends
% 0.76/1.16 *** allocated 10000 integers for clauses
% 0.76/1.16 *** allocated 10000 integers for justifications
% 0.76/1.16 Bliksem 1.12
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 Automatic Strategy Selection
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 Clauses:
% 0.76/1.16
% 0.76/1.16 { ! distinct_points( X, X ) }.
% 0.76/1.16 { ! distinct_lines( X, X ) }.
% 0.76/1.16 { ! convergent_lines( X, X ) }.
% 0.76/1.16 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 0.76/1.16 ) }.
% 0.76/1.16 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.76/1.16 }.
% 0.76/1.16 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 0.76/1.16 , Z ) }.
% 0.76/1.16 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 0.76/1.16 , Y ) ) }.
% 0.76/1.16 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 0.76/1.16 , Y ) ) }.
% 0.76/1.16 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.76/1.16 , Y ), X ) }.
% 0.76/1.16 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.76/1.16 , Y ), Y ) }.
% 0.76/1.16 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 0.76/1.16 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 0.76/1.16 apart_point_and_line( Y, T ) }.
% 0.76/1.16 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 0.76/1.16 apart_point_and_line( Z, Y ) }.
% 0.76/1.16 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 0.76/1.16 apart_point_and_line( X, Z ) }.
% 0.76/1.16 { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X,
% 0.76/1.16 Z ) }.
% 0.76/1.16 { ! distinct_lines( X, Y ), convergent_lines( X, Y ) }.
% 0.76/1.16 { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 0.76/1.16 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 0.76/1.16 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 0.76/1.16 apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 0.76/1.16 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.76/1.16 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.76/1.16 , convergent_lines( Y, Z ) }.
% 0.76/1.16 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.76/1.16 , unorthogonal_lines( Y, Z ) }.
% 0.76/1.16 { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 0.76/1.16 { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.76/1.16 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 0.76/1.16 }.
% 0.76/1.16 { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 0.76/1.16 { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 0.76/1.16 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 0.76/1.16 apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ),
% 0.76/1.16 unorthogonal_lines( Y, T ) }.
% 0.76/1.16 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.76/1.16 { alpha2( X, Z ), convergent_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 0.76/1.16 unorthogonal_lines( X, Y ) }.
% 0.76/1.16 { alpha2( X, Z ), unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 0.76/1.16 unorthogonal_lines( X, Y ) }.
% 0.76/1.16 { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 0.76/1.16 { ! alpha2( X, Y ), unorthogonal_lines( Y, X ) }.
% 0.76/1.16 { ! convergent_lines( Y, X ), ! unorthogonal_lines( Y, X ), alpha2( X, Y )
% 0.76/1.16 }.
% 0.76/1.16 { unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ), !
% 0.76/1.16 convergent_lines( X, Y ) }.
% 0.76/1.16 { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line(
% 0.76/1.16 line_connecting( X, Y ) ) }.
% 0.76/1.16 { ! line( X ), ! line( Y ), ! convergent_lines( X, Y ), point(
% 0.76/1.16 intersection_point( X, Y ) ) }.
% 0.76/1.16 { ! line( X ), ! point( Y ), line( parallel_through_point( X, Y ) ) }.
% 0.76/1.16 { ! line( X ), ! point( Y ), line( orthogonal_through_point( X, Y ) ) }.
% 0.76/1.16 { ! equal_points( X, Y ), ! distinct_points( X, Y ) }.
% 0.76/1.16 { distinct_points( X, Y ), equal_points( X, Y ) }.
% 0.76/1.16 { ! equal_lines( X, Y ), ! distinct_lines( X, Y ) }.
% 0.76/1.16 { distinct_lines( X, Y ), equal_lines( X, Y ) }.
% 0.76/1.16 { ! parallel_lines( X, Y ), ! convergent_lines( X, Y ) }.
% 0.76/1.16 { convergent_lines( X, Y ), parallel_lines( X, Y ) }.
% 0.76/1.16 { ! incident_point_and_line( X, Y ), ! apart_point_and_line( X, Y ) }.
% 0.76/1.16 { apart_point_and_line( X, Y ), incident_point_and_line( X, Y ) }.
% 0.76/1.16 { ! orthogonal_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.76/1.16 { unorthogonal_lines( X, Y ), orthogonal_lines( X, Y ) }.
% 0.76/1.16 { ! equal_lines( parallel_through_point( skol2, skol1 ),
% 0.76/1.16 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 0.76/1.16 ) ) }.
% 0.76/1.16
% 0.76/1.16 percentage equality = 0.000000, percentage horn = 0.595745
% 0.76/1.16 This a non-horn, non-equality problem
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 Options Used:
% 0.76/1.16
% 0.76/1.16 useres = 1
% 0.76/1.16 useparamod = 0
% 0.76/1.16 useeqrefl = 0
% 0.76/1.16 useeqfact = 0
% 0.76/1.16 usefactor = 1
% 0.76/1.16 usesimpsplitting = 0
% 0.76/1.16 usesimpdemod = 0
% 0.76/1.16 usesimpres = 3
% 0.76/1.16
% 0.76/1.16 resimpinuse = 1000
% 0.76/1.16 resimpclauses = 20000
% 0.76/1.16 substype = standard
% 0.76/1.16 backwardsubs = 1
% 0.76/1.16 selectoldest = 5
% 0.76/1.16
% 0.76/1.16 litorderings [0] = split
% 0.76/1.16 litorderings [1] = liftord
% 0.76/1.16
% 0.76/1.16 termordering = none
% 0.76/1.16
% 0.76/1.16 litapriori = 1
% 0.76/1.16 termapriori = 0
% 0.76/1.16 litaposteriori = 0
% 0.76/1.16 termaposteriori = 0
% 0.76/1.16 demodaposteriori = 0
% 0.76/1.16 ordereqreflfact = 0
% 0.76/1.16
% 0.76/1.16 litselect = none
% 0.76/1.16
% 0.76/1.16 maxweight = 15
% 0.76/1.16 maxdepth = 30000
% 0.76/1.16 maxlength = 115
% 0.76/1.16 maxnrvars = 195
% 0.76/1.16 excuselevel = 1
% 0.76/1.16 increasemaxweight = 1
% 0.76/1.16
% 0.76/1.16 maxselected = 10000000
% 0.76/1.16 maxnrclauses = 10000000
% 0.76/1.16
% 0.76/1.16 showgenerated = 0
% 0.76/1.16 showkept = 0
% 0.76/1.16 showselected = 0
% 0.76/1.16 showdeleted = 0
% 0.76/1.16 showresimp = 1
% 0.76/1.16 showstatus = 2000
% 0.76/1.16
% 0.76/1.16 prologoutput = 0
% 0.76/1.16 nrgoals = 5000000
% 0.76/1.16 totalproof = 1
% 0.76/1.16
% 0.76/1.16 Symbols occurring in the translation:
% 0.76/1.16
% 0.76/1.16 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.76/1.16 . [1, 2] (w:1, o:25, a:1, s:1, b:0),
% 0.76/1.16 ! [4, 1] (w:0, o:18, a:1, s:1, b:0),
% 0.76/1.16 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.76/1.16 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.76/1.16 distinct_points [36, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.76/1.16 distinct_lines [37, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.76/1.16 convergent_lines [38, 2] (w:1, o:49, a:1, s:1, b:0),
% 0.76/1.16 line_connecting [41, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.76/1.16 apart_point_and_line [42, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.76/1.16 intersection_point [43, 2] (w:1, o:54, a:1, s:1, b:0),
% 0.76/1.16 parallel_through_point [46, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.76/1.16 unorthogonal_lines [49, 2] (w:1, o:58, a:1, s:1, b:0),
% 0.76/1.16 orthogonal_through_point [52, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.76/1.16 point [54, 1] (w:1, o:23, a:1, s:1, b:0),
% 0.76/1.16 line [55, 1] (w:1, o:24, a:1, s:1, b:0),
% 0.76/1.16 equal_points [56, 2] (w:1, o:59, a:1, s:1, b:0),
% 0.76/1.16 equal_lines [57, 2] (w:1, o:60, a:1, s:1, b:0),
% 0.76/1.16 parallel_lines [58, 2] (w:1, o:61, a:1, s:1, b:0),
% 0.76/1.16 incident_point_and_line [59, 2] (w:1, o:62, a:1, s:1, b:0),
% 0.76/1.16 orthogonal_lines [60, 2] (w:1, o:56, a:1, s:1, b:0),
% 0.76/1.16 alpha1 [61, 2] (w:1, o:63, a:1, s:1, b:0),
% 0.76/1.16 alpha2 [62, 2] (w:1, o:64, a:1, s:1, b:0),
% 0.76/1.16 skol1 [63, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.76/1.16 skol2 [64, 0] (w:1, o:17, a:1, s:1, b:0).
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 Starting Search:
% 0.76/1.16
% 0.76/1.16 *** allocated 15000 integers for clauses
% 0.76/1.16 *** allocated 22500 integers for clauses
% 0.76/1.16 *** allocated 33750 integers for clauses
% 0.76/1.16 *** allocated 15000 integers for termspace/termends
% 0.76/1.16 *** allocated 50625 integers for clauses
% 0.76/1.16 Resimplifying inuse:
% 0.76/1.16 Done
% 0.76/1.16
% 0.76/1.16 *** allocated 22500 integers for termspace/termends
% 0.76/1.16 *** allocated 75937 integers for clauses
% 0.76/1.16 *** allocated 33750 integers for termspace/termends
% 0.76/1.16 *** allocated 113905 integers for clauses
% 0.76/1.16
% 0.76/1.16 Intermediate Status:
% 0.76/1.16 Generated: 22044
% 0.76/1.16 Kept: 2001
% 0.76/1.16 Inuse: 318
% 0.76/1.16 Deleted: 6
% 0.76/1.16 Deletedinuse: 3
% 0.76/1.16
% 0.76/1.16 Resimplifying inuse:
% 0.76/1.16 Done
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 Bliksems!, er is een bewijs:
% 0.76/1.16 % SZS status Theorem
% 0.76/1.16 % SZS output start Refutation
% 0.76/1.16
% 0.76/1.16 (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.76/1.16 (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.76/1.16 (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.76/1.16 , ! distinct_lines( X, Y ) }.
% 0.76/1.16 (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), convergent_lines( Y,
% 0.76/1.16 Z ), ! convergent_lines( X, Y ) }.
% 0.76/1.16 (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! distinct_lines( X
% 0.76/1.16 , Y ) }.
% 0.76/1.16 (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines( parallel_through_point( Y
% 0.76/1.16 , X ), Y ) }.
% 0.76/1.16 (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), unorthogonal_lines(
% 0.76/1.16 X, Y ) }.
% 0.76/1.16 (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 0.76/1.16 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 0.76/1.16 }.
% 0.76/1.16 (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! alpha1( X, Y ) }.
% 0.76/1.16 (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( orthogonal_through_point
% 0.76/1.16 ( Y, X ), Y ) }.
% 0.76/1.16 (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ), unorthogonal_lines
% 0.76/1.16 ( Z, X ), unorthogonal_lines( Z, Y ) }.
% 0.76/1.16 (39) {G0,W6,D2,L2,V2,M1} I { distinct_lines( X, Y ), equal_lines( X, Y )
% 0.76/1.16 }.
% 0.76/1.16 (46) {G0,W9,D4,L1,V0,M1} I { ! equal_lines( parallel_through_point( skol2,
% 0.76/1.16 skol1 ), orthogonal_through_point( orthogonal_through_point( skol2, skol1
% 0.76/1.16 ), skol1 ) ) }.
% 0.76/1.16 (55) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 0.76/1.16 ( X, Y ) }.
% 0.76/1.16 (61) {G1,W8,D3,L2,V3,M2} R(5,15) { ! convergent_lines( X,
% 0.76/1.16 parallel_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 0.76/1.16 (62) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.76/1.16 convergent_lines( X, Y ) }.
% 0.76/1.16 (69) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 0.76/1.16 orthogonal_through_point( X, Y ), X ) }.
% 0.76/1.16 (71) {G2,W8,D3,L2,V3,M2} R(69,5) { convergent_lines( X, Z ),
% 0.76/1.16 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.76/1.16 (72) {G2,W6,D2,L2,V2,M1} R(14,55) { convergent_lines( X, Y ), !
% 0.76/1.16 distinct_lines( Y, X ) }.
% 0.76/1.16 (79) {G3,W8,D3,L2,V3,M2} R(71,62) { convergent_lines( Z, X ),
% 0.76/1.16 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.76/1.16 (145) {G4,W8,D3,L2,V3,M2} R(79,62) { convergent_lines( X,
% 0.76/1.16 orthogonal_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 0.76/1.16 (213) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y ),
% 0.76/1.16 convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 0.76/1.16 unorthogonal_lines( Y, Z ) }.
% 0.76/1.16 (316) {G1,W8,D3,L2,V3,M1} R(31,23) { ! convergent_lines( X, Y ),
% 0.76/1.16 unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 0.76/1.16 (381) {G1,W9,D4,L1,V0,M1} R(46,39) { distinct_lines( parallel_through_point
% 0.76/1.16 ( skol2, skol1 ), orthogonal_through_point( orthogonal_through_point(
% 0.76/1.16 skol2, skol1 ), skol1 ) ) }.
% 0.76/1.16 (600) {G3,W9,D4,L1,V0,M1} R(381,72) { convergent_lines(
% 0.76/1.16 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 0.76/1.16 ), parallel_through_point( skol2, skol1 ) ) }.
% 0.76/1.16 (604) {G4,W7,D4,L1,V0,M1} R(600,61) { convergent_lines(
% 0.76/1.16 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 0.76/1.16 ), skol2 ) }.
% 0.76/1.16 (2089) {G5,W8,D3,L2,V3,M1} R(213,23);r(145) { convergent_lines( X, Y ), !
% 0.76/1.16 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 0.76/1.16 (2096) {G6,W10,D3,L2,V4,M2} R(2089,316) { ! convergent_lines(
% 0.76/1.16 orthogonal_through_point( Z, T ), X ), convergent_lines(
% 0.76/1.16 orthogonal_through_point( X, Y ), Z ) }.
% 0.76/1.16 (2242) {G7,W7,D3,L1,V1,M1} R(2096,604) { convergent_lines(
% 0.76/1.16 orthogonal_through_point( skol2, X ), orthogonal_through_point( skol2,
% 0.76/1.16 skol1 ) ) }.
% 0.76/1.16 (2276) {G7,W7,D4,L1,V3,M1} R(2096,2) { ! convergent_lines(
% 0.76/1.16 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 0.76/1.16 (2279) {G8,W0,D0,L0,V0,M0} R(2242,2096);r(2276) { }.
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 % SZS output end Refutation
% 0.76/1.16 found a proof!
% 0.76/1.16
% 0.76/1.16 *** allocated 50625 integers for termspace/termends
% 0.76/1.16
% 0.76/1.16 Unprocessed initial clauses:
% 0.76/1.16
% 0.76/1.16 (2281) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 0.76/1.16 (2282) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.76/1.16 (2283) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 0.76/1.16 (2284) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 0.76/1.16 , Z ), distinct_points( Y, Z ) }.
% 0.76/1.16 (2285) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X,
% 0.76/1.16 Z ), distinct_lines( Y, Z ) }.
% 0.76/1.16 (2286) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines
% 0.76/1.16 ( X, Z ), convergent_lines( Y, Z ) }.
% 0.76/1.16 (2287) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.76/1.16 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 0.76/1.16 (2288) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.76/1.16 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 0.76/1.16 (2289) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 0.76/1.16 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 0.76/1.16 (2290) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 0.76/1.16 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 0.76/1.16 (2291) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines
% 0.76/1.16 ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 0.76/1.16 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 0.76/1.16 (2292) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 0.76/1.16 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 0.76/1.16 (2293) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 0.76/1.16 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 0.76/1.16 (2294) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), distinct_lines( Y
% 0.76/1.16 , Z ), convergent_lines( X, Z ) }.
% 0.76/1.16 (2295) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ), convergent_lines( X
% 0.76/1.16 , Y ) }.
% 0.76/1.16 (2296) {G0,W5,D3,L1,V2,M1} { ! convergent_lines( parallel_through_point( Y
% 0.76/1.16 , X ), Y ) }.
% 0.76/1.16 (2297) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.76/1.16 parallel_through_point( Y, X ) ) }.
% 0.76/1.16 (2298) {G0,W12,D2,L4,V3,M4} { ! distinct_lines( X, Y ),
% 0.76/1.16 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 0.76/1.16 convergent_lines( X, Y ) }.
% 0.76/1.16 (2299) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines
% 0.76/1.16 ( X, Y ) }.
% 0.76/1.16 (2300) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.76/1.16 unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 0.76/1.16 (2301) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.76/1.16 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 0.76/1.16 }.
% 0.76/1.16 (2302) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines( X, Y )
% 0.76/1.16 }.
% 0.76/1.16 (2303) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 0.76/1.16 }.
% 0.76/1.16 (2304) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( X, Y ), !
% 0.76/1.16 unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 0.76/1.16 (2305) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines(
% 0.76/1.16 orthogonal_through_point( Y, X ), Y ) }.
% 0.76/1.16 (2306) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.76/1.16 orthogonal_through_point( Y, X ) ) }.
% 0.76/1.16 (2307) {G0,W15,D2,L5,V4,M5} { ! distinct_lines( X, Y ),
% 0.76/1.16 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 0.76/1.16 unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 0.76/1.16 (2308) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines
% 0.76/1.16 ( X, Y ) }.
% 0.76/1.16 (2309) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), convergent_lines( Z, Y ), !
% 0.76/1.16 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.76/1.16 (2310) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), unorthogonal_lines( Z, Y ),
% 0.76/1.16 ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.76/1.16 (2311) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), convergent_lines( Y, X )
% 0.76/1.16 }.
% 0.76/1.16 (2312) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), unorthogonal_lines( Y, X )
% 0.76/1.16 }.
% 0.76/1.16 (2313) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( Y, X ), !
% 0.76/1.16 unorthogonal_lines( Y, X ), alpha2( X, Y ) }.
% 0.76/1.16 (2314) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ),
% 0.76/1.16 unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 0.76/1.16 (2315) {G0,W11,D3,L4,V2,M4} { ! point( X ), ! point( Y ), !
% 0.76/1.16 distinct_points( X, Y ), line( line_connecting( X, Y ) ) }.
% 0.76/1.16 (2316) {G0,W11,D3,L4,V2,M4} { ! line( X ), ! line( Y ), ! convergent_lines
% 0.76/1.16 ( X, Y ), point( intersection_point( X, Y ) ) }.
% 0.76/1.16 (2317) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 0.76/1.16 parallel_through_point( X, Y ) ) }.
% 0.76/1.16 (2318) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 0.76/1.16 orthogonal_through_point( X, Y ) ) }.
% 0.76/1.16 (2319) {G0,W6,D2,L2,V2,M2} { ! equal_points( X, Y ), ! distinct_points( X
% 0.76/1.16 , Y ) }.
% 0.76/1.16 (2320) {G0,W6,D2,L2,V2,M2} { distinct_points( X, Y ), equal_points( X, Y )
% 0.76/1.16 }.
% 0.76/1.16 (2321) {G0,W6,D2,L2,V2,M2} { ! equal_lines( X, Y ), ! distinct_lines( X, Y
% 0.76/1.16 ) }.
% 0.76/1.16 (2322) {G0,W6,D2,L2,V2,M2} { distinct_lines( X, Y ), equal_lines( X, Y )
% 0.76/1.16 }.
% 0.76/1.16 (2323) {G0,W6,D2,L2,V2,M2} { ! parallel_lines( X, Y ), ! convergent_lines
% 0.76/1.16 ( X, Y ) }.
% 0.76/1.16 (2324) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), parallel_lines( X,
% 0.76/1.16 Y ) }.
% 0.76/1.16 (2325) {G0,W6,D2,L2,V2,M2} { ! incident_point_and_line( X, Y ), !
% 0.76/1.16 apart_point_and_line( X, Y ) }.
% 0.76/1.16 (2326) {G0,W6,D2,L2,V2,M2} { apart_point_and_line( X, Y ),
% 0.76/1.16 incident_point_and_line( X, Y ) }.
% 0.76/1.16 (2327) {G0,W6,D2,L2,V2,M2} { ! orthogonal_lines( X, Y ), !
% 0.76/1.16 unorthogonal_lines( X, Y ) }.
% 0.76/1.16 (2328) {G0,W6,D2,L2,V2,M2} { unorthogonal_lines( X, Y ), orthogonal_lines
% 0.76/1.16 ( X, Y ) }.
% 0.76/1.16 (2329) {G0,W9,D4,L1,V0,M1} { ! equal_lines( parallel_through_point( skol2
% 0.76/1.16 , skol1 ), orthogonal_through_point( orthogonal_through_point( skol2,
% 0.76/1.16 skol1 ), skol1 ) ) }.
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 Total Proof:
% 0.76/1.16
% 0.76/1.16 subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.76/1.16 parent0: (2282) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := X
% 0.76/1.16 end
% 0.76/1.16 permutation0:
% 0.76/1.16 0 ==> 0
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 subsumption: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.76/1.16 parent0: (2283) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := X
% 0.76/1.16 end
% 0.76/1.16 permutation0:
% 0.76/1.16 0 ==> 0
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 0.76/1.16 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 0.76/1.16 parent0: (2285) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ),
% 0.76/1.16 distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := X
% 0.76/1.16 Y := Y
% 0.76/1.16 Z := Z
% 0.76/1.16 end
% 0.76/1.16 permutation0:
% 0.76/1.16 0 ==> 2
% 0.76/1.16 1 ==> 0
% 0.76/1.16 2 ==> 1
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 subsumption: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 0.76/1.16 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.76/1.16 parent0: (2286) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 0.76/1.16 convergent_lines( X, Z ), convergent_lines( Y, Z ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := X
% 0.76/1.16 Y := Y
% 0.76/1.16 Z := Z
% 0.76/1.16 end
% 0.76/1.16 permutation0:
% 0.76/1.16 0 ==> 2
% 0.76/1.16 1 ==> 0
% 0.76/1.16 2 ==> 1
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 subsumption: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 0.76/1.16 distinct_lines( X, Y ) }.
% 0.76/1.16 parent0: (2295) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ),
% 0.76/1.16 convergent_lines( X, Y ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := X
% 0.76/1.16 Y := Y
% 0.76/1.16 end
% 0.76/1.16 permutation0:
% 0.76/1.16 0 ==> 1
% 0.76/1.16 1 ==> 0
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 subsumption: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 0.76/1.16 parallel_through_point( Y, X ), Y ) }.
% 0.76/1.16 parent0: (2296) {G0,W5,D3,L1,V2,M1} { ! convergent_lines(
% 0.76/1.16 parallel_through_point( Y, X ), Y ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := X
% 0.76/1.16 Y := Y
% 0.76/1.16 end
% 0.76/1.16 permutation0:
% 0.76/1.16 0 ==> 0
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 subsumption: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 0.76/1.16 unorthogonal_lines( X, Y ) }.
% 0.76/1.16 parent0: (2299) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ),
% 0.76/1.16 unorthogonal_lines( X, Y ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := X
% 0.76/1.16 Y := Y
% 0.76/1.16 end
% 0.76/1.16 permutation0:
% 0.76/1.16 0 ==> 0
% 0.76/1.16 1 ==> 1
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 subsumption: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 0.76/1.16 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 0.76/1.16 }.
% 0.76/1.16 parent0: (2301) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.76/1.16 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 0.76/1.16 }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := X
% 0.76/1.16 Y := Y
% 0.76/1.16 Z := Z
% 0.76/1.16 end
% 0.76/1.16 permutation0:
% 0.76/1.16 0 ==> 0
% 0.76/1.16 1 ==> 1
% 0.76/1.16 2 ==> 3
% 0.76/1.16 3 ==> 2
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 subsumption: (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 0.76/1.16 alpha1( X, Y ) }.
% 0.76/1.16 parent0: (2302) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines(
% 0.76/1.16 X, Y ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := X
% 0.76/1.16 Y := Y
% 0.76/1.16 end
% 0.76/1.16 permutation0:
% 0.76/1.16 0 ==> 1
% 0.76/1.16 1 ==> 0
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 subsumption: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 0.76/1.16 orthogonal_through_point( Y, X ), Y ) }.
% 0.76/1.16 parent0: (2305) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines(
% 0.76/1.16 orthogonal_through_point( Y, X ), Y ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := X
% 0.76/1.16 Y := Y
% 0.76/1.16 end
% 0.76/1.16 permutation0:
% 0.76/1.16 0 ==> 0
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 subsumption: (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ),
% 0.76/1.16 unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ) }.
% 0.76/1.16 parent0: (2314) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ),
% 0.76/1.16 unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := X
% 0.76/1.16 Y := Y
% 0.76/1.16 Z := Z
% 0.76/1.16 end
% 0.76/1.16 permutation0:
% 0.76/1.16 0 ==> 1
% 0.76/1.16 1 ==> 2
% 0.76/1.16 2 ==> 0
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 subsumption: (39) {G0,W6,D2,L2,V2,M1} I { distinct_lines( X, Y ),
% 0.76/1.16 equal_lines( X, Y ) }.
% 0.76/1.16 parent0: (2322) {G0,W6,D2,L2,V2,M2} { distinct_lines( X, Y ), equal_lines
% 0.76/1.16 ( X, Y ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := X
% 0.76/1.16 Y := Y
% 0.76/1.16 end
% 0.76/1.16 permutation0:
% 0.76/1.16 0 ==> 0
% 0.76/1.16 1 ==> 1
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 subsumption: (46) {G0,W9,D4,L1,V0,M1} I { ! equal_lines(
% 0.76/1.16 parallel_through_point( skol2, skol1 ), orthogonal_through_point(
% 0.76/1.16 orthogonal_through_point( skol2, skol1 ), skol1 ) ) }.
% 0.76/1.16 parent0: (2329) {G0,W9,D4,L1,V0,M1} { ! equal_lines(
% 0.76/1.16 parallel_through_point( skol2, skol1 ), orthogonal_through_point(
% 0.76/1.16 orthogonal_through_point( skol2, skol1 ), skol1 ) ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 end
% 0.76/1.16 permutation0:
% 0.76/1.16 0 ==> 0
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 resolution: (2436) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 0.76/1.16 distinct_lines( X, Y ) }.
% 0.76/1.16 parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.76/1.16 parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 0.76/1.16 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := X
% 0.76/1.16 end
% 0.76/1.16 substitution1:
% 0.76/1.16 X := X
% 0.76/1.16 Y := Y
% 0.76/1.16 Z := X
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 subsumption: (55) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 0.76/1.16 distinct_lines( X, Y ) }.
% 0.76/1.16 parent0: (2436) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 0.76/1.16 distinct_lines( X, Y ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := Y
% 0.76/1.16 Y := X
% 0.76/1.16 end
% 0.76/1.16 permutation0:
% 0.76/1.16 0 ==> 1
% 0.76/1.16 1 ==> 0
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 resolution: (2439) {G1,W8,D3,L2,V3,M2} { convergent_lines( Z, X ), !
% 0.76/1.16 convergent_lines( Z, parallel_through_point( X, Y ) ) }.
% 0.76/1.16 parent0[0]: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 0.76/1.16 parallel_through_point( Y, X ), Y ) }.
% 0.76/1.16 parent1[1]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 0.76/1.16 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := Y
% 0.76/1.16 Y := X
% 0.76/1.16 end
% 0.76/1.16 substitution1:
% 0.76/1.16 X := Z
% 0.76/1.16 Y := parallel_through_point( X, Y )
% 0.76/1.16 Z := X
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 subsumption: (61) {G1,W8,D3,L2,V3,M2} R(5,15) { ! convergent_lines( X,
% 0.76/1.16 parallel_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 0.76/1.16 parent0: (2439) {G1,W8,D3,L2,V3,M2} { convergent_lines( Z, X ), !
% 0.76/1.16 convergent_lines( Z, parallel_through_point( X, Y ) ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := Y
% 0.76/1.16 Y := Z
% 0.76/1.16 Z := X
% 0.76/1.16 end
% 0.76/1.16 permutation0:
% 0.76/1.16 0 ==> 1
% 0.76/1.16 1 ==> 0
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 resolution: (2440) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 0.76/1.16 convergent_lines( X, Y ) }.
% 0.76/1.16 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.76/1.16 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 0.76/1.16 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := X
% 0.76/1.16 end
% 0.76/1.16 substitution1:
% 0.76/1.16 X := X
% 0.76/1.16 Y := Y
% 0.76/1.16 Z := X
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 subsumption: (62) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.76/1.16 convergent_lines( X, Y ) }.
% 0.76/1.16 parent0: (2440) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 0.76/1.16 convergent_lines( X, Y ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := Y
% 0.76/1.16 Y := X
% 0.76/1.16 end
% 0.76/1.16 permutation0:
% 0.76/1.16 0 ==> 1
% 0.76/1.16 1 ==> 0
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 resolution: (2442) {G1,W5,D3,L1,V2,M1} { convergent_lines(
% 0.76/1.16 orthogonal_through_point( X, Y ), X ) }.
% 0.76/1.16 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 0.76/1.16 orthogonal_through_point( Y, X ), Y ) }.
% 0.76/1.16 parent1[1]: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 0.76/1.16 unorthogonal_lines( X, Y ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := Y
% 0.76/1.16 Y := X
% 0.76/1.16 end
% 0.76/1.16 substitution1:
% 0.76/1.16 X := orthogonal_through_point( X, Y )
% 0.76/1.16 Y := X
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 subsumption: (69) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 0.76/1.16 orthogonal_through_point( X, Y ), X ) }.
% 0.76/1.16 parent0: (2442) {G1,W5,D3,L1,V2,M1} { convergent_lines(
% 0.76/1.16 orthogonal_through_point( X, Y ), X ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := X
% 0.76/1.16 Y := Y
% 0.76/1.16 end
% 0.76/1.16 permutation0:
% 0.76/1.16 0 ==> 0
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 resolution: (2443) {G1,W8,D3,L2,V3,M2} { convergent_lines(
% 0.76/1.16 orthogonal_through_point( X, Y ), Z ), convergent_lines( X, Z ) }.
% 0.76/1.16 parent0[2]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 0.76/1.16 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.76/1.16 parent1[0]: (69) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 0.76/1.16 orthogonal_through_point( X, Y ), X ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := orthogonal_through_point( X, Y )
% 0.76/1.16 Y := X
% 0.76/1.16 Z := Z
% 0.76/1.16 end
% 0.76/1.16 substitution1:
% 0.76/1.16 X := X
% 0.76/1.16 Y := Y
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 subsumption: (71) {G2,W8,D3,L2,V3,M2} R(69,5) { convergent_lines( X, Z ),
% 0.76/1.16 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.76/1.16 parent0: (2443) {G1,W8,D3,L2,V3,M2} { convergent_lines(
% 0.76/1.16 orthogonal_through_point( X, Y ), Z ), convergent_lines( X, Z ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := X
% 0.76/1.16 Y := Y
% 0.76/1.16 Z := Z
% 0.76/1.16 end
% 0.76/1.16 permutation0:
% 0.76/1.16 0 ==> 1
% 0.76/1.16 1 ==> 0
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 resolution: (2444) {G1,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), !
% 0.76/1.16 distinct_lines( Y, X ) }.
% 0.76/1.16 parent0[1]: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 0.76/1.16 distinct_lines( X, Y ) }.
% 0.76/1.16 parent1[1]: (55) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 0.76/1.16 distinct_lines( X, Y ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := X
% 0.76/1.16 Y := Y
% 0.76/1.16 end
% 0.76/1.16 substitution1:
% 0.76/1.16 X := X
% 0.76/1.16 Y := Y
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 subsumption: (72) {G2,W6,D2,L2,V2,M1} R(14,55) { convergent_lines( X, Y ),
% 0.76/1.16 ! distinct_lines( Y, X ) }.
% 0.76/1.16 parent0: (2444) {G1,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), !
% 0.76/1.16 distinct_lines( Y, X ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := X
% 0.76/1.16 Y := Y
% 0.76/1.16 end
% 0.76/1.16 permutation0:
% 0.76/1.16 0 ==> 0
% 0.76/1.16 1 ==> 1
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 resolution: (2445) {G2,W8,D3,L2,V3,M2} { convergent_lines( Y, X ),
% 0.76/1.16 convergent_lines( orthogonal_through_point( X, Z ), Y ) }.
% 0.76/1.16 parent0[0]: (62) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.76/1.16 convergent_lines( X, Y ) }.
% 0.76/1.16 parent1[0]: (71) {G2,W8,D3,L2,V3,M2} R(69,5) { convergent_lines( X, Z ),
% 0.76/1.16 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := Y
% 0.76/1.16 Y := X
% 0.76/1.16 end
% 0.76/1.16 substitution1:
% 0.76/1.16 X := X
% 0.76/1.16 Y := Z
% 0.76/1.16 Z := Y
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 subsumption: (79) {G3,W8,D3,L2,V3,M2} R(71,62) { convergent_lines( Z, X ),
% 0.76/1.16 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.76/1.16 parent0: (2445) {G2,W8,D3,L2,V3,M2} { convergent_lines( Y, X ),
% 0.76/1.16 convergent_lines( orthogonal_through_point( X, Z ), Y ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := X
% 0.76/1.16 Y := Z
% 0.76/1.16 Z := Y
% 0.76/1.16 end
% 0.76/1.16 permutation0:
% 0.76/1.16 0 ==> 0
% 0.76/1.16 1 ==> 1
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 resolution: (2448) {G2,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 0.76/1.16 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ) }.
% 0.76/1.16 parent0[0]: (62) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.76/1.16 convergent_lines( X, Y ) }.
% 0.76/1.16 parent1[1]: (79) {G3,W8,D3,L2,V3,M2} R(71,62) { convergent_lines( Z, X ),
% 0.76/1.16 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := Z
% 0.76/1.16 Y := orthogonal_through_point( X, Y )
% 0.76/1.16 end
% 0.76/1.16 substitution1:
% 0.76/1.16 X := X
% 0.76/1.16 Y := Y
% 0.76/1.16 Z := Z
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 subsumption: (145) {G4,W8,D3,L2,V3,M2} R(79,62) { convergent_lines( X,
% 0.76/1.16 orthogonal_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 0.76/1.16 parent0: (2448) {G2,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 0.76/1.16 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := Y
% 0.76/1.16 Y := Z
% 0.76/1.16 Z := X
% 0.76/1.16 end
% 0.76/1.16 permutation0:
% 0.76/1.16 0 ==> 0
% 0.76/1.16 1 ==> 1
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 resolution: (2450) {G1,W12,D2,L4,V3,M4} { convergent_lines( X, Y ), !
% 0.76/1.16 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ),
% 0.76/1.16 unorthogonal_lines( Z, Y ) }.
% 0.76/1.16 parent0[1]: (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! alpha1
% 0.76/1.16 ( X, Y ) }.
% 0.76/1.16 parent1[3]: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 0.76/1.16 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 0.76/1.16 }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := X
% 0.76/1.16 Y := Y
% 0.76/1.16 end
% 0.76/1.16 substitution1:
% 0.76/1.16 X := X
% 0.76/1.16 Y := Z
% 0.76/1.16 Z := Y
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 subsumption: (213) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y
% 0.76/1.16 ), convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 0.76/1.16 unorthogonal_lines( Y, Z ) }.
% 0.76/1.16 parent0: (2450) {G1,W12,D2,L4,V3,M4} { convergent_lines( X, Y ), !
% 0.76/1.16 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ),
% 0.76/1.16 unorthogonal_lines( Z, Y ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := X
% 0.76/1.16 Y := Z
% 0.76/1.16 Z := Y
% 0.76/1.16 end
% 0.76/1.16 permutation0:
% 0.76/1.16 0 ==> 1
% 0.76/1.16 1 ==> 0
% 0.76/1.16 2 ==> 2
% 0.76/1.16 3 ==> 3
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 resolution: (2452) {G1,W8,D3,L2,V3,M2} { ! convergent_lines( Z, X ),
% 0.76/1.16 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.76/1.16 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 0.76/1.16 orthogonal_through_point( Y, X ), Y ) }.
% 0.76/1.16 parent1[2]: (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ),
% 0.76/1.16 unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := Y
% 0.76/1.16 Y := X
% 0.76/1.16 end
% 0.76/1.16 substitution1:
% 0.76/1.16 X := Z
% 0.76/1.16 Y := X
% 0.76/1.16 Z := orthogonal_through_point( X, Y )
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 subsumption: (316) {G1,W8,D3,L2,V3,M1} R(31,23) { ! convergent_lines( X, Y
% 0.76/1.16 ), unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 0.76/1.16 parent0: (2452) {G1,W8,D3,L2,V3,M2} { ! convergent_lines( Z, X ),
% 0.76/1.16 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := Y
% 0.76/1.16 Y := Z
% 0.76/1.16 Z := X
% 0.76/1.16 end
% 0.76/1.16 permutation0:
% 0.76/1.16 0 ==> 0
% 0.76/1.16 1 ==> 1
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 resolution: (2453) {G1,W9,D4,L1,V0,M1} { distinct_lines(
% 0.76/1.16 parallel_through_point( skol2, skol1 ), orthogonal_through_point(
% 0.76/1.16 orthogonal_through_point( skol2, skol1 ), skol1 ) ) }.
% 0.76/1.16 parent0[0]: (46) {G0,W9,D4,L1,V0,M1} I { ! equal_lines(
% 0.76/1.16 parallel_through_point( skol2, skol1 ), orthogonal_through_point(
% 0.76/1.16 orthogonal_through_point( skol2, skol1 ), skol1 ) ) }.
% 0.76/1.16 parent1[1]: (39) {G0,W6,D2,L2,V2,M1} I { distinct_lines( X, Y ),
% 0.76/1.16 equal_lines( X, Y ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 end
% 0.76/1.16 substitution1:
% 0.76/1.16 X := parallel_through_point( skol2, skol1 )
% 0.76/1.16 Y := orthogonal_through_point( orthogonal_through_point( skol2, skol1 )
% 0.76/1.16 , skol1 )
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 subsumption: (381) {G1,W9,D4,L1,V0,M1} R(46,39) { distinct_lines(
% 0.76/1.16 parallel_through_point( skol2, skol1 ), orthogonal_through_point(
% 0.76/1.16 orthogonal_through_point( skol2, skol1 ), skol1 ) ) }.
% 0.76/1.16 parent0: (2453) {G1,W9,D4,L1,V0,M1} { distinct_lines(
% 0.76/1.16 parallel_through_point( skol2, skol1 ), orthogonal_through_point(
% 0.76/1.16 orthogonal_through_point( skol2, skol1 ), skol1 ) ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 end
% 0.76/1.16 permutation0:
% 0.76/1.16 0 ==> 0
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 resolution: (2454) {G2,W9,D4,L1,V0,M1} { convergent_lines(
% 0.76/1.16 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 0.76/1.16 ), parallel_through_point( skol2, skol1 ) ) }.
% 0.76/1.16 parent0[1]: (72) {G2,W6,D2,L2,V2,M1} R(14,55) { convergent_lines( X, Y ), !
% 0.76/1.16 distinct_lines( Y, X ) }.
% 0.76/1.16 parent1[0]: (381) {G1,W9,D4,L1,V0,M1} R(46,39) { distinct_lines(
% 0.76/1.16 parallel_through_point( skol2, skol1 ), orthogonal_through_point(
% 0.76/1.16 orthogonal_through_point( skol2, skol1 ), skol1 ) ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := orthogonal_through_point( orthogonal_through_point( skol2, skol1 )
% 0.76/1.16 , skol1 )
% 0.76/1.16 Y := parallel_through_point( skol2, skol1 )
% 0.76/1.16 end
% 0.76/1.16 substitution1:
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 subsumption: (600) {G3,W9,D4,L1,V0,M1} R(381,72) { convergent_lines(
% 0.76/1.16 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 0.76/1.16 ), parallel_through_point( skol2, skol1 ) ) }.
% 0.76/1.16 parent0: (2454) {G2,W9,D4,L1,V0,M1} { convergent_lines(
% 0.76/1.16 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 0.76/1.16 ), parallel_through_point( skol2, skol1 ) ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 end
% 0.76/1.16 permutation0:
% 0.76/1.16 0 ==> 0
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 resolution: (2455) {G2,W7,D4,L1,V0,M1} { convergent_lines(
% 0.76/1.16 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 0.76/1.16 ), skol2 ) }.
% 0.76/1.16 parent0[0]: (61) {G1,W8,D3,L2,V3,M2} R(5,15) { ! convergent_lines( X,
% 0.76/1.16 parallel_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 0.76/1.16 parent1[0]: (600) {G3,W9,D4,L1,V0,M1} R(381,72) { convergent_lines(
% 0.76/1.16 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 0.76/1.16 ), parallel_through_point( skol2, skol1 ) ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := orthogonal_through_point( orthogonal_through_point( skol2, skol1 )
% 0.76/1.16 , skol1 )
% 0.76/1.16 Y := skol2
% 0.76/1.16 Z := skol1
% 0.76/1.16 end
% 0.76/1.16 substitution1:
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 subsumption: (604) {G4,W7,D4,L1,V0,M1} R(600,61) { convergent_lines(
% 0.76/1.16 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 0.76/1.16 ), skol2 ) }.
% 0.76/1.16 parent0: (2455) {G2,W7,D4,L1,V0,M1} { convergent_lines(
% 0.76/1.16 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 0.76/1.16 ), skol2 ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 end
% 0.76/1.16 permutation0:
% 0.76/1.16 0 ==> 0
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 resolution: (2456) {G1,W13,D3,L3,V3,M3} { ! convergent_lines( Z,
% 0.76/1.16 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ), !
% 0.76/1.16 unorthogonal_lines( Z, orthogonal_through_point( X, Y ) ) }.
% 0.76/1.16 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 0.76/1.16 orthogonal_through_point( Y, X ), Y ) }.
% 0.76/1.16 parent1[3]: (213) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y
% 0.76/1.16 ), convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 0.76/1.16 unorthogonal_lines( Y, Z ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := Y
% 0.76/1.16 Y := X
% 0.76/1.16 end
% 0.76/1.16 substitution1:
% 0.76/1.16 X := Z
% 0.76/1.16 Y := orthogonal_through_point( X, Y )
% 0.76/1.16 Z := X
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 resolution: (2457) {G2,W11,D3,L3,V3,M3} { convergent_lines( X, Y ), !
% 0.76/1.16 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ),
% 0.76/1.16 convergent_lines( X, Y ) }.
% 0.76/1.16 parent0[0]: (2456) {G1,W13,D3,L3,V3,M3} { ! convergent_lines( Z,
% 0.76/1.16 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ), !
% 0.76/1.16 unorthogonal_lines( Z, orthogonal_through_point( X, Y ) ) }.
% 0.76/1.16 parent1[0]: (145) {G4,W8,D3,L2,V3,M2} R(79,62) { convergent_lines( X,
% 0.76/1.16 orthogonal_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := Y
% 0.76/1.16 Y := Z
% 0.76/1.16 Z := X
% 0.76/1.16 end
% 0.76/1.16 substitution1:
% 0.76/1.16 X := X
% 0.76/1.16 Y := Y
% 0.76/1.16 Z := Z
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 factor: (2458) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 0.76/1.16 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 0.76/1.16 parent0[0, 2]: (2457) {G2,W11,D3,L3,V3,M3} { convergent_lines( X, Y ), !
% 0.76/1.16 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ),
% 0.76/1.16 convergent_lines( X, Y ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := X
% 0.76/1.16 Y := Y
% 0.76/1.16 Z := Z
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 subsumption: (2089) {G5,W8,D3,L2,V3,M1} R(213,23);r(145) { convergent_lines
% 0.76/1.16 ( X, Y ), ! unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 0.76/1.16 parent0: (2458) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 0.76/1.16 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := X
% 0.76/1.16 Y := Y
% 0.76/1.16 Z := Z
% 0.76/1.16 end
% 0.76/1.16 permutation0:
% 0.76/1.16 0 ==> 0
% 0.76/1.16 1 ==> 1
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 resolution: (2459) {G2,W10,D3,L2,V4,M2} { convergent_lines(
% 0.76/1.16 orthogonal_through_point( X, Y ), Z ), ! convergent_lines(
% 0.76/1.16 orthogonal_through_point( Z, T ), X ) }.
% 0.76/1.16 parent0[1]: (2089) {G5,W8,D3,L2,V3,M1} R(213,23);r(145) { convergent_lines
% 0.76/1.16 ( X, Y ), ! unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 0.76/1.16 parent1[1]: (316) {G1,W8,D3,L2,V3,M1} R(31,23) { ! convergent_lines( X, Y )
% 0.76/1.16 , unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := orthogonal_through_point( X, Y )
% 0.76/1.16 Y := Z
% 0.76/1.16 Z := T
% 0.76/1.16 end
% 0.76/1.16 substitution1:
% 0.76/1.16 X := orthogonal_through_point( Z, T )
% 0.76/1.16 Y := X
% 0.76/1.16 Z := Y
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 subsumption: (2096) {G6,W10,D3,L2,V4,M2} R(2089,316) { ! convergent_lines(
% 0.76/1.16 orthogonal_through_point( Z, T ), X ), convergent_lines(
% 0.76/1.16 orthogonal_through_point( X, Y ), Z ) }.
% 0.76/1.16 parent0: (2459) {G2,W10,D3,L2,V4,M2} { convergent_lines(
% 0.76/1.16 orthogonal_through_point( X, Y ), Z ), ! convergent_lines(
% 0.76/1.16 orthogonal_through_point( Z, T ), X ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := X
% 0.76/1.16 Y := Y
% 0.76/1.16 Z := Z
% 0.76/1.16 T := T
% 0.76/1.16 end
% 0.76/1.16 permutation0:
% 0.76/1.16 0 ==> 1
% 0.76/1.16 1 ==> 0
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 resolution: (2460) {G5,W7,D3,L1,V1,M1} { convergent_lines(
% 0.76/1.16 orthogonal_through_point( skol2, X ), orthogonal_through_point( skol2,
% 0.76/1.16 skol1 ) ) }.
% 0.76/1.16 parent0[0]: (2096) {G6,W10,D3,L2,V4,M2} R(2089,316) { ! convergent_lines(
% 0.76/1.16 orthogonal_through_point( Z, T ), X ), convergent_lines(
% 0.76/1.16 orthogonal_through_point( X, Y ), Z ) }.
% 0.76/1.16 parent1[0]: (604) {G4,W7,D4,L1,V0,M1} R(600,61) { convergent_lines(
% 0.76/1.16 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 0.76/1.16 ), skol2 ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := skol2
% 0.76/1.16 Y := X
% 0.76/1.16 Z := orthogonal_through_point( skol2, skol1 )
% 0.76/1.16 T := skol1
% 0.76/1.16 end
% 0.76/1.16 substitution1:
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 subsumption: (2242) {G7,W7,D3,L1,V1,M1} R(2096,604) { convergent_lines(
% 0.76/1.16 orthogonal_through_point( skol2, X ), orthogonal_through_point( skol2,
% 0.76/1.16 skol1 ) ) }.
% 0.76/1.16 parent0: (2460) {G5,W7,D3,L1,V1,M1} { convergent_lines(
% 0.76/1.16 orthogonal_through_point( skol2, X ), orthogonal_through_point( skol2,
% 0.76/1.16 skol1 ) ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := X
% 0.76/1.16 end
% 0.76/1.16 permutation0:
% 0.76/1.16 0 ==> 0
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 resolution: (2461) {G1,W7,D4,L1,V3,M1} { ! convergent_lines(
% 0.76/1.16 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 0.76/1.16 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.76/1.16 parent1[1]: (2096) {G6,W10,D3,L2,V4,M2} R(2089,316) { ! convergent_lines(
% 0.76/1.16 orthogonal_through_point( Z, T ), X ), convergent_lines(
% 0.76/1.16 orthogonal_through_point( X, Y ), Z ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := orthogonal_through_point( X, Y )
% 0.76/1.16 end
% 0.76/1.16 substitution1:
% 0.76/1.16 X := X
% 0.76/1.16 Y := Y
% 0.76/1.16 Z := orthogonal_through_point( X, Y )
% 0.76/1.16 T := Z
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 subsumption: (2276) {G7,W7,D4,L1,V3,M1} R(2096,2) { ! convergent_lines(
% 0.76/1.16 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 0.76/1.16 parent0: (2461) {G1,W7,D4,L1,V3,M1} { ! convergent_lines(
% 0.76/1.16 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := X
% 0.76/1.16 Y := Y
% 0.76/1.16 Z := Z
% 0.76/1.16 end
% 0.76/1.16 permutation0:
% 0.76/1.16 0 ==> 0
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 resolution: (2462) {G7,W7,D4,L1,V1,M1} { convergent_lines(
% 0.76/1.16 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), Y ),
% 0.76/1.16 skol2 ) }.
% 0.76/1.16 parent0[0]: (2096) {G6,W10,D3,L2,V4,M2} R(2089,316) { ! convergent_lines(
% 0.76/1.16 orthogonal_through_point( Z, T ), X ), convergent_lines(
% 0.76/1.16 orthogonal_through_point( X, Y ), Z ) }.
% 0.76/1.16 parent1[0]: (2242) {G7,W7,D3,L1,V1,M1} R(2096,604) { convergent_lines(
% 0.76/1.16 orthogonal_through_point( skol2, X ), orthogonal_through_point( skol2,
% 0.76/1.16 skol1 ) ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := orthogonal_through_point( skol2, skol1 )
% 0.76/1.16 Y := Y
% 0.76/1.16 Z := skol2
% 0.76/1.16 T := X
% 0.76/1.16 end
% 0.76/1.16 substitution1:
% 0.76/1.16 X := X
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 resolution: (2463) {G8,W0,D0,L0,V0,M0} { }.
% 0.76/1.16 parent0[0]: (2276) {G7,W7,D4,L1,V3,M1} R(2096,2) { ! convergent_lines(
% 0.76/1.16 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 0.76/1.16 parent1[0]: (2462) {G7,W7,D4,L1,V1,M1} { convergent_lines(
% 0.76/1.16 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), Y ),
% 0.76/1.16 skol2 ) }.
% 0.76/1.16 substitution0:
% 0.76/1.16 X := skol2
% 0.76/1.16 Y := skol1
% 0.76/1.16 Z := X
% 0.76/1.16 end
% 0.76/1.16 substitution1:
% 0.76/1.16 X := Y
% 0.76/1.16 Y := X
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 subsumption: (2279) {G8,W0,D0,L0,V0,M0} R(2242,2096);r(2276) { }.
% 0.76/1.16 parent0: (2463) {G8,W0,D0,L0,V0,M0} { }.
% 0.76/1.16 substitution0:
% 0.76/1.16 end
% 0.76/1.16 permutation0:
% 0.76/1.16 end
% 0.76/1.16
% 0.76/1.16 Proof check complete!
% 0.76/1.16
% 0.76/1.16 Memory use:
% 0.76/1.16
% 0.76/1.16 space for terms: 33424
% 0.76/1.16 space for clauses: 94775
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 clauses generated: 25223
% 0.76/1.16 clauses kept: 2280
% 0.76/1.16 clauses selected: 355
% 0.76/1.16 clauses deleted: 8
% 0.76/1.16 clauses inuse deleted: 3
% 0.76/1.16
% 0.76/1.16 subsentry: 526218
% 0.76/1.16 literals s-matched: 235875
% 0.76/1.16 literals matched: 235817
% 0.76/1.16 full subsumption: 159844
% 0.76/1.16
% 0.76/1.16 checksum: 2059309153
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 Bliksem ended
%------------------------------------------------------------------------------