%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO221+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Sat Jul 16 02:52:57 EDT 2022
% Result : Theorem 0.85s 1.26s
% Output : Refutation 0.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GEO221+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.14 % Command : bliksem %s
% 0.12/0.35 % Computer : n027.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % DateTime : Sat Jun 18 18:50:38 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.85/1.26 *** allocated 10000 integers for termspace/termends
% 0.85/1.26 *** allocated 10000 integers for clauses
% 0.85/1.26 *** allocated 10000 integers for justifications
% 0.85/1.26 Bliksem 1.12
% 0.85/1.26
% 0.85/1.26
% 0.85/1.26 Automatic Strategy Selection
% 0.85/1.26
% 0.85/1.26
% 0.85/1.26 Clauses:
% 0.85/1.26
% 0.85/1.26 { ! distinct_points( X, X ) }.
% 0.85/1.26 { ! distinct_lines( X, X ) }.
% 0.85/1.26 { ! convergent_lines( X, X ) }.
% 0.85/1.26 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 0.85/1.26 ) }.
% 0.85/1.26 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.85/1.26 }.
% 0.85/1.26 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 0.85/1.26 , Z ) }.
% 0.85/1.26 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 0.85/1.26 , Y ) ) }.
% 0.85/1.26 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 0.85/1.26 , Y ) ) }.
% 0.85/1.26 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.85/1.26 , Y ), X ) }.
% 0.85/1.26 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.85/1.26 , Y ), Y ) }.
% 0.85/1.26 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 0.85/1.26 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 0.85/1.26 apart_point_and_line( Y, T ) }.
% 0.85/1.26 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 0.85/1.26 apart_point_and_line( Z, Y ) }.
% 0.85/1.26 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 0.85/1.26 apart_point_and_line( X, Z ) }.
% 0.85/1.26 { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X,
% 0.85/1.26 Z ) }.
% 0.85/1.26 { ! distinct_lines( X, Y ), convergent_lines( X, Y ) }.
% 0.85/1.26 { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 0.85/1.26 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 0.85/1.26 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 0.85/1.26 apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 0.85/1.26 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.85/1.26 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.85/1.26 , convergent_lines( Y, Z ) }.
% 0.85/1.26 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.85/1.26 , unorthogonal_lines( Y, Z ) }.
% 0.85/1.26 { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 0.85/1.26 { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.85/1.26 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 0.85/1.26 }.
% 0.85/1.26 { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 0.85/1.26 { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 0.85/1.26 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 0.85/1.26 apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ),
% 0.85/1.26 unorthogonal_lines( Y, T ) }.
% 0.85/1.26 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.85/1.26 { alpha2( X, Z ), convergent_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 0.85/1.26 unorthogonal_lines( X, Y ) }.
% 0.85/1.26 { alpha2( X, Z ), unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 0.85/1.26 unorthogonal_lines( X, Y ) }.
% 0.85/1.26 { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 0.85/1.26 { ! alpha2( X, Y ), unorthogonal_lines( Y, X ) }.
% 0.85/1.26 { ! convergent_lines( Y, X ), ! unorthogonal_lines( Y, X ), alpha2( X, Y )
% 0.85/1.26 }.
% 0.85/1.26 { unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ), !
% 0.85/1.26 convergent_lines( X, Y ) }.
% 0.85/1.26 { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line(
% 0.85/1.26 line_connecting( X, Y ) ) }.
% 0.85/1.26 { ! line( X ), ! line( Y ), ! convergent_lines( X, Y ), point(
% 0.85/1.26 intersection_point( X, Y ) ) }.
% 0.85/1.26 { ! line( X ), ! point( Y ), line( parallel_through_point( X, Y ) ) }.
% 0.85/1.26 { ! line( X ), ! point( Y ), line( orthogonal_through_point( X, Y ) ) }.
% 0.85/1.26 { ! equal_points( X, Y ), ! distinct_points( X, Y ) }.
% 0.85/1.26 { distinct_points( X, Y ), equal_points( X, Y ) }.
% 0.85/1.26 { ! equal_lines( X, Y ), ! distinct_lines( X, Y ) }.
% 0.85/1.26 { distinct_lines( X, Y ), equal_lines( X, Y ) }.
% 0.85/1.26 { ! parallel_lines( X, Y ), ! convergent_lines( X, Y ) }.
% 0.85/1.26 { convergent_lines( X, Y ), parallel_lines( X, Y ) }.
% 0.85/1.26 { ! incident_point_and_line( X, Y ), ! apart_point_and_line( X, Y ) }.
% 0.85/1.26 { apart_point_and_line( X, Y ), incident_point_and_line( X, Y ) }.
% 0.85/1.26 { ! orthogonal_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.85/1.26 { unorthogonal_lines( X, Y ), orthogonal_lines( X, Y ) }.
% 0.85/1.26 { incident_point_and_line( skol2, orthogonal_through_point( skol3, skol1 )
% 0.85/1.26 ) }.
% 0.85/1.26 { ! equal_lines( orthogonal_through_point( skol3, skol1 ),
% 0.85/1.26 orthogonal_through_point( skol3, skol2 ) ) }.
% 0.85/1.26
% 0.85/1.26 percentage equality = 0.000000, percentage horn = 0.604167
% 0.85/1.26 This a non-horn, non-equality problem
% 0.85/1.26
% 0.85/1.26
% 0.85/1.26 Options Used:
% 0.85/1.26
% 0.85/1.26 useres = 1
% 0.85/1.26 useparamod = 0
% 0.85/1.26 useeqrefl = 0
% 0.85/1.26 useeqfact = 0
% 0.85/1.26 usefactor = 1
% 0.85/1.26 usesimpsplitting = 0
% 0.85/1.26 usesimpdemod = 0
% 0.85/1.26 usesimpres = 3
% 0.85/1.26
% 0.85/1.26 resimpinuse = 1000
% 0.85/1.26 resimpclauses = 20000
% 0.85/1.26 substype = standard
% 0.85/1.26 backwardsubs = 1
% 0.85/1.26 selectoldest = 5
% 0.85/1.26
% 0.85/1.26 litorderings [0] = split
% 0.85/1.26 litorderings [1] = liftord
% 0.85/1.26
% 0.85/1.26 termordering = none
% 0.85/1.26
% 0.85/1.26 litapriori = 1
% 0.85/1.26 termapriori = 0
% 0.85/1.26 litaposteriori = 0
% 0.85/1.26 termaposteriori = 0
% 0.85/1.26 demodaposteriori = 0
% 0.85/1.26 ordereqreflfact = 0
% 0.85/1.26
% 0.85/1.26 litselect = none
% 0.85/1.26
% 0.85/1.26 maxweight = 15
% 0.85/1.26 maxdepth = 30000
% 0.85/1.26 maxlength = 115
% 0.85/1.26 maxnrvars = 195
% 0.85/1.26 excuselevel = 1
% 0.85/1.26 increasemaxweight = 1
% 0.85/1.26
% 0.85/1.26 maxselected = 10000000
% 0.85/1.26 maxnrclauses = 10000000
% 0.85/1.26
% 0.85/1.26 showgenerated = 0
% 0.85/1.26 showkept = 0
% 0.85/1.26 showselected = 0
% 0.85/1.26 showdeleted = 0
% 0.85/1.26 showresimp = 1
% 0.85/1.26 showstatus = 2000
% 0.85/1.26
% 0.85/1.26 prologoutput = 0
% 0.85/1.26 nrgoals = 5000000
% 0.85/1.26 totalproof = 1
% 0.85/1.26
% 0.85/1.26 Symbols occurring in the translation:
% 0.85/1.26
% 0.85/1.26 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.85/1.26 . [1, 2] (w:1, o:26, a:1, s:1, b:0),
% 0.85/1.26 ! [4, 1] (w:0, o:19, a:1, s:1, b:0),
% 0.85/1.26 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.85/1.26 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.85/1.26 distinct_points [36, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.85/1.26 distinct_lines [37, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.85/1.26 convergent_lines [38, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.85/1.26 line_connecting [41, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.85/1.26 apart_point_and_line [42, 2] (w:1, o:54, a:1, s:1, b:0),
% 0.85/1.26 intersection_point [43, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.85/1.26 parallel_through_point [46, 2] (w:1, o:58, a:1, s:1, b:0),
% 0.85/1.26 unorthogonal_lines [49, 2] (w:1, o:59, a:1, s:1, b:0),
% 0.85/1.26 orthogonal_through_point [52, 2] (w:1, o:56, a:1, s:1, b:0),
% 0.85/1.26 point [54, 1] (w:1, o:24, a:1, s:1, b:0),
% 0.85/1.26 line [55, 1] (w:1, o:25, a:1, s:1, b:0),
% 0.85/1.26 equal_points [56, 2] (w:1, o:60, a:1, s:1, b:0),
% 0.85/1.26 equal_lines [57, 2] (w:1, o:61, a:1, s:1, b:0),
% 0.85/1.26 parallel_lines [58, 2] (w:1, o:62, a:1, s:1, b:0),
% 0.85/1.26 incident_point_and_line [59, 2] (w:1, o:63, a:1, s:1, b:0),
% 0.85/1.26 orthogonal_lines [60, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.85/1.26 alpha1 [61, 2] (w:1, o:64, a:1, s:1, b:0),
% 0.85/1.26 alpha2 [62, 2] (w:1, o:65, a:1, s:1, b:0),
% 0.85/1.26 skol1 [63, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.85/1.26 skol2 [64, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.85/1.26 skol3 [65, 0] (w:1, o:18, a:1, s:1, b:0).
% 0.85/1.26
% 0.85/1.26
% 0.85/1.26 Starting Search:
% 0.85/1.26
% 0.85/1.26 *** allocated 15000 integers for clauses
% 0.85/1.26 *** allocated 22500 integers for clauses
% 0.85/1.26 *** allocated 33750 integers for clauses
% 0.85/1.26 *** allocated 15000 integers for termspace/termends
% 0.85/1.26 *** allocated 50625 integers for clauses
% 0.85/1.26 Resimplifying inuse:
% 0.85/1.26 Done
% 0.85/1.26
% 0.85/1.26 *** allocated 22500 integers for termspace/termends
% 0.85/1.26 *** allocated 75937 integers for clauses
% 0.85/1.26 *** allocated 33750 integers for termspace/termends
% 0.85/1.26 *** allocated 113905 integers for clauses
% 0.85/1.26
% 0.85/1.26 Intermediate Status:
% 0.85/1.26 Generated: 21826
% 0.85/1.26 Kept: 2041
% 0.85/1.26 Inuse: 323
% 0.85/1.26 Deleted: 2
% 0.85/1.26 Deletedinuse: 2
% 0.85/1.26
% 0.85/1.26 Resimplifying inuse:
% 0.85/1.26 Done
% 0.85/1.26
% 0.85/1.26 *** allocated 50625 integers for termspace/termends
% 0.85/1.26
% 0.85/1.26 Bliksems!, er is een bewijs:
% 0.85/1.26 % SZS status Theorem
% 0.85/1.26 % SZS output start Refutation
% 0.85/1.26
% 0.85/1.26 (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.85/1.26 (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.85/1.26 (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.85/1.26 , ! distinct_lines( X, Y ) }.
% 0.85/1.26 (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), convergent_lines( Y,
% 0.85/1.26 Z ), ! convergent_lines( X, Y ) }.
% 0.85/1.26 (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! distinct_lines( X
% 0.85/1.26 , Y ) }.
% 0.85/1.26 (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), unorthogonal_lines(
% 0.85/1.26 X, Y ) }.
% 0.85/1.26 (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 0.85/1.26 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 0.85/1.26 }.
% 0.85/1.26 (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! alpha1( X, Y ) }.
% 0.85/1.26 (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( orthogonal_through_point
% 0.85/1.26 ( Y, X ), Y ) }.
% 0.85/1.26 (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ), unorthogonal_lines
% 0.85/1.26 ( Z, X ), unorthogonal_lines( Z, Y ) }.
% 0.85/1.26 (39) {G0,W6,D2,L2,V2,M1} I { distinct_lines( X, Y ), equal_lines( X, Y )
% 0.85/1.26 }.
% 0.85/1.26 (47) {G0,W7,D3,L1,V0,M1} I { ! equal_lines( orthogonal_through_point( skol3
% 0.85/1.26 , skol1 ), orthogonal_through_point( skol3, skol2 ) ) }.
% 0.85/1.26 (55) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 0.85/1.26 ( X, Y ) }.
% 0.85/1.26 (63) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.85/1.26 convergent_lines( X, Y ) }.
% 0.85/1.26 (71) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 0.85/1.26 orthogonal_through_point( X, Y ), X ) }.
% 0.85/1.26 (73) {G2,W8,D3,L2,V3,M2} R(71,5) { convergent_lines( X, Z ),
% 0.85/1.26 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.85/1.26 (74) {G2,W6,D2,L2,V2,M1} R(14,55) { convergent_lines( X, Y ), !
% 0.85/1.26 distinct_lines( Y, X ) }.
% 0.85/1.26 (105) {G1,W7,D3,L1,V0,M1} R(47,39) { distinct_lines(
% 0.85/1.26 orthogonal_through_point( skol3, skol1 ), orthogonal_through_point( skol3
% 0.85/1.26 , skol2 ) ) }.
% 0.85/1.26 (106) {G3,W7,D3,L1,V0,M1} R(105,74) { convergent_lines(
% 0.85/1.26 orthogonal_through_point( skol3, skol2 ), orthogonal_through_point( skol3
% 0.85/1.26 , skol1 ) ) }.
% 0.85/1.26 (110) {G4,W10,D3,L2,V1,M1} R(106,5) { convergent_lines(
% 0.85/1.26 orthogonal_through_point( skol3, skol1 ), X ), convergent_lines(
% 0.85/1.26 orthogonal_through_point( skol3, skol2 ), X ) }.
% 0.85/1.26 (144) {G3,W8,D3,L2,V3,M2} R(73,63) { convergent_lines( Z, X ),
% 0.85/1.26 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.85/1.26 (158) {G4,W8,D3,L2,V3,M2} R(144,63) { convergent_lines( X,
% 0.85/1.26 orthogonal_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 0.85/1.26 (161) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y ),
% 0.85/1.26 convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 0.85/1.26 unorthogonal_lines( Y, Z ) }.
% 0.85/1.26 (305) {G1,W8,D3,L2,V3,M1} R(31,23) { ! convergent_lines( X, Y ),
% 0.85/1.26 unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 0.85/1.26 (2148) {G5,W8,D3,L2,V3,M1} R(161,23);r(158) { convergent_lines( X, Y ), !
% 0.85/1.26 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 0.85/1.26 (2155) {G6,W10,D3,L2,V4,M2} R(2148,305) { ! convergent_lines(
% 0.85/1.26 orthogonal_through_point( Z, T ), X ), convergent_lines(
% 0.85/1.26 orthogonal_through_point( X, Y ), Z ) }.
% 0.85/1.26 (2334) {G7,W7,D4,L1,V3,M1} R(2155,2) { ! convergent_lines(
% 0.85/1.26 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 0.85/1.26 (2337) {G8,W7,D3,L1,V3,M1} R(2334,2155) { ! convergent_lines(
% 0.85/1.26 orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ) }.
% 0.85/1.26 (2484) {G9,W0,D0,L0,V0,M0} R(2337,110);r(2337) { }.
% 0.85/1.26
% 0.85/1.26
% 0.85/1.26 % SZS output end Refutation
% 0.85/1.26 found a proof!
% 0.85/1.26
% 0.85/1.26
% 0.85/1.26 Unprocessed initial clauses:
% 0.85/1.26
% 0.85/1.26 (2486) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 0.85/1.26 (2487) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.85/1.26 (2488) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 0.85/1.26 (2489) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 0.85/1.26 , Z ), distinct_points( Y, Z ) }.
% 0.85/1.26 (2490) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X,
% 0.85/1.26 Z ), distinct_lines( Y, Z ) }.
% 0.85/1.26 (2491) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines
% 0.85/1.26 ( X, Z ), convergent_lines( Y, Z ) }.
% 0.85/1.26 (2492) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.85/1.26 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 0.85/1.26 (2493) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.85/1.26 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 0.85/1.26 (2494) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 0.85/1.26 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 0.85/1.26 (2495) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 0.85/1.26 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 0.85/1.26 (2496) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines
% 0.85/1.26 ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 0.85/1.26 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 0.85/1.26 (2497) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 0.85/1.26 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 0.85/1.26 (2498) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 0.85/1.26 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 0.85/1.26 (2499) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), distinct_lines( Y
% 0.85/1.26 , Z ), convergent_lines( X, Z ) }.
% 0.85/1.26 (2500) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ), convergent_lines( X
% 0.85/1.26 , Y ) }.
% 0.85/1.26 (2501) {G0,W5,D3,L1,V2,M1} { ! convergent_lines( parallel_through_point( Y
% 0.85/1.26 , X ), Y ) }.
% 0.85/1.26 (2502) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.85/1.26 parallel_through_point( Y, X ) ) }.
% 0.85/1.26 (2503) {G0,W12,D2,L4,V3,M4} { ! distinct_lines( X, Y ),
% 0.85/1.26 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 0.85/1.26 convergent_lines( X, Y ) }.
% 0.85/1.26 (2504) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines
% 0.85/1.26 ( X, Y ) }.
% 0.85/1.26 (2505) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.85/1.26 unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 0.85/1.26 (2506) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.85/1.26 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 0.85/1.26 }.
% 0.85/1.26 (2507) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines( X, Y )
% 0.85/1.26 }.
% 0.85/1.26 (2508) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 0.85/1.26 }.
% 0.85/1.26 (2509) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( X, Y ), !
% 0.85/1.26 unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 0.85/1.26 (2510) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines(
% 0.85/1.26 orthogonal_through_point( Y, X ), Y ) }.
% 0.85/1.26 (2511) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.85/1.26 orthogonal_through_point( Y, X ) ) }.
% 0.85/1.26 (2512) {G0,W15,D2,L5,V4,M5} { ! distinct_lines( X, Y ),
% 0.85/1.26 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 0.85/1.26 unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 0.85/1.26 (2513) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines
% 0.85/1.26 ( X, Y ) }.
% 0.85/1.26 (2514) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), convergent_lines( Z, Y ), !
% 0.85/1.26 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.85/1.26 (2515) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), unorthogonal_lines( Z, Y ),
% 0.85/1.26 ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.85/1.26 (2516) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), convergent_lines( Y, X )
% 0.85/1.26 }.
% 0.85/1.26 (2517) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), unorthogonal_lines( Y, X )
% 0.85/1.26 }.
% 0.85/1.26 (2518) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( Y, X ), !
% 0.85/1.26 unorthogonal_lines( Y, X ), alpha2( X, Y ) }.
% 0.85/1.26 (2519) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ),
% 0.85/1.26 unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 0.85/1.26 (2520) {G0,W11,D3,L4,V2,M4} { ! point( X ), ! point( Y ), !
% 0.85/1.26 distinct_points( X, Y ), line( line_connecting( X, Y ) ) }.
% 0.85/1.26 (2521) {G0,W11,D3,L4,V2,M4} { ! line( X ), ! line( Y ), ! convergent_lines
% 0.85/1.26 ( X, Y ), point( intersection_point( X, Y ) ) }.
% 0.85/1.26 (2522) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 0.85/1.26 parallel_through_point( X, Y ) ) }.
% 0.85/1.26 (2523) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 0.85/1.26 orthogonal_through_point( X, Y ) ) }.
% 0.85/1.26 (2524) {G0,W6,D2,L2,V2,M2} { ! equal_points( X, Y ), ! distinct_points( X
% 0.85/1.26 , Y ) }.
% 0.85/1.26 (2525) {G0,W6,D2,L2,V2,M2} { distinct_points( X, Y ), equal_points( X, Y )
% 0.85/1.26 }.
% 0.85/1.26 (2526) {G0,W6,D2,L2,V2,M2} { ! equal_lines( X, Y ), ! distinct_lines( X, Y
% 0.85/1.26 ) }.
% 0.85/1.26 (2527) {G0,W6,D2,L2,V2,M2} { distinct_lines( X, Y ), equal_lines( X, Y )
% 0.85/1.26 }.
% 0.85/1.26 (2528) {G0,W6,D2,L2,V2,M2} { ! parallel_lines( X, Y ), ! convergent_lines
% 0.85/1.26 ( X, Y ) }.
% 0.85/1.26 (2529) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), parallel_lines( X,
% 0.85/1.26 Y ) }.
% 0.85/1.26 (2530) {G0,W6,D2,L2,V2,M2} { ! incident_point_and_line( X, Y ), !
% 0.85/1.26 apart_point_and_line( X, Y ) }.
% 0.85/1.26 (2531) {G0,W6,D2,L2,V2,M2} { apart_point_and_line( X, Y ),
% 0.85/1.26 incident_point_and_line( X, Y ) }.
% 0.85/1.26 (2532) {G0,W6,D2,L2,V2,M2} { ! orthogonal_lines( X, Y ), !
% 0.85/1.26 unorthogonal_lines( X, Y ) }.
% 0.85/1.26 (2533) {G0,W6,D2,L2,V2,M2} { unorthogonal_lines( X, Y ), orthogonal_lines
% 0.85/1.26 ( X, Y ) }.
% 0.85/1.26 (2534) {G0,W5,D3,L1,V0,M1} { incident_point_and_line( skol2,
% 0.85/1.26 orthogonal_through_point( skol3, skol1 ) ) }.
% 0.85/1.26 (2535) {G0,W7,D3,L1,V0,M1} { ! equal_lines( orthogonal_through_point(
% 0.85/1.26 skol3, skol1 ), orthogonal_through_point( skol3, skol2 ) ) }.
% 0.85/1.26
% 0.85/1.26
% 0.85/1.26 Total Proof:
% 0.85/1.26
% 0.85/1.26 subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.85/1.26 parent0: (2487) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.85/1.26 substitution0:
% 0.85/1.26 X := X
% 0.85/1.26 end
% 0.85/1.26 permutation0:
% 0.85/1.26 0 ==> 0
% 0.85/1.26 end
% 0.85/1.26
% 0.85/1.26 subsumption: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.85/1.26 parent0: (2488) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 0.85/1.26 substitution0:
% 0.85/1.26 X := X
% 0.85/1.26 end
% 0.85/1.26 permutation0:
% 0.85/1.26 0 ==> 0
% 0.85/1.26 end
% 0.85/1.26
% 0.85/1.26 subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 0.85/1.26 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 0.85/1.26 parent0: (2490) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ),
% 0.85/1.26 distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 0.85/1.26 substitution0:
% 0.85/1.26 X := X
% 0.85/1.26 Y := Y
% 0.85/1.26 Z := Z
% 0.85/1.26 end
% 0.85/1.26 permutation0:
% 0.85/1.26 0 ==> 2
% 0.85/1.26 1 ==> 0
% 0.85/1.26 2 ==> 1
% 0.85/1.26 end
% 0.85/1.26
% 0.85/1.26 subsumption: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 0.85/1.26 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.85/1.26 parent0: (2491) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 0.85/1.26 convergent_lines( X, Z ), convergent_lines( Y, Z ) }.
% 0.85/1.26 substitution0:
% 0.85/1.26 X := X
% 0.85/1.26 Y := Y
% 0.85/1.26 Z := Z
% 0.85/1.26 end
% 0.85/1.26 permutation0:
% 0.85/1.26 0 ==> 2
% 0.85/1.26 1 ==> 0
% 0.85/1.26 2 ==> 1
% 0.85/1.26 end
% 0.85/1.26
% 0.85/1.26 subsumption: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 0.85/1.26 distinct_lines( X, Y ) }.
% 0.85/1.26 parent0: (2500) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ),
% 0.85/1.26 convergent_lines( X, Y ) }.
% 0.85/1.26 substitution0:
% 0.85/1.26 X := X
% 0.85/1.26 Y := Y
% 0.85/1.26 end
% 0.85/1.26 permutation0:
% 0.85/1.26 0 ==> 1
% 0.85/1.26 1 ==> 0
% 0.85/1.26 end
% 0.85/1.26
% 0.85/1.26 subsumption: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 0.85/1.26 unorthogonal_lines( X, Y ) }.
% 0.85/1.26 parent0: (2504) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ),
% 0.85/1.26 unorthogonal_lines( X, Y ) }.
% 0.85/1.26 substitution0:
% 0.85/1.26 X := X
% 0.85/1.26 Y := Y
% 0.85/1.26 end
% 0.85/1.26 permutation0:
% 0.85/1.26 0 ==> 0
% 0.85/1.26 1 ==> 1
% 0.85/1.26 end
% 0.85/1.26
% 0.85/1.26 subsumption: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 0.85/1.26 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 0.85/1.26 }.
% 0.85/1.26 parent0: (2506) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.85/1.26 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 0.85/1.26 }.
% 0.85/1.26 substitution0:
% 0.85/1.26 X := X
% 0.85/1.26 Y := Y
% 0.85/1.26 Z := Z
% 0.85/1.26 end
% 0.85/1.26 permutation0:
% 0.85/1.26 0 ==> 0
% 0.85/1.26 1 ==> 1
% 0.85/1.26 2 ==> 3
% 0.85/1.26 3 ==> 2
% 0.85/1.26 end
% 0.85/1.26
% 0.85/1.26 subsumption: (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 0.85/1.26 alpha1( X, Y ) }.
% 0.85/1.26 parent0: (2507) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines(
% 0.85/1.26 X, Y ) }.
% 0.85/1.26 substitution0:
% 0.85/1.26 X := X
% 0.85/1.26 Y := Y
% 0.85/1.26 end
% 0.85/1.26 permutation0:
% 0.85/1.26 0 ==> 1
% 0.85/1.26 1 ==> 0
% 0.85/1.26 end
% 0.85/1.26
% 0.85/1.26 subsumption: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 0.85/1.26 orthogonal_through_point( Y, X ), Y ) }.
% 0.85/1.26 parent0: (2510) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines(
% 0.85/1.26 orthogonal_through_point( Y, X ), Y ) }.
% 0.85/1.26 substitution0:
% 0.85/1.26 X := X
% 0.85/1.26 Y := Y
% 0.85/1.26 end
% 0.85/1.26 permutation0:
% 0.85/1.26 0 ==> 0
% 0.85/1.26 end
% 0.85/1.26
% 0.85/1.26 subsumption: (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ),
% 0.85/1.26 unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ) }.
% 0.85/1.26 parent0: (2519) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ),
% 0.85/1.26 unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 0.85/1.26 substitution0:
% 0.85/1.26 X := X
% 0.85/1.26 Y := Y
% 0.85/1.26 Z := Z
% 0.85/1.26 end
% 0.85/1.26 permutation0:
% 0.85/1.26 0 ==> 1
% 0.85/1.26 1 ==> 2
% 0.85/1.26 2 ==> 0
% 0.85/1.26 end
% 0.85/1.26
% 0.85/1.26 subsumption: (39) {G0,W6,D2,L2,V2,M1} I { distinct_lines( X, Y ),
% 0.85/1.26 equal_lines( X, Y ) }.
% 0.85/1.26 parent0: (2527) {G0,W6,D2,L2,V2,M2} { distinct_lines( X, Y ), equal_lines
% 0.85/1.26 ( X, Y ) }.
% 0.85/1.26 substitution0:
% 0.85/1.26 X := X
% 0.85/1.26 Y := Y
% 0.85/1.26 end
% 0.85/1.26 permutation0:
% 0.85/1.26 0 ==> 0
% 0.85/1.26 1 ==> 1
% 0.85/1.26 end
% 0.85/1.26
% 0.85/1.26 subsumption: (47) {G0,W7,D3,L1,V0,M1} I { ! equal_lines(
% 0.85/1.26 orthogonal_through_point( skol3, skol1 ), orthogonal_through_point( skol3
% 0.85/1.26 , skol2 ) ) }.
% 0.85/1.26 parent0: (2535) {G0,W7,D3,L1,V0,M1} { ! equal_lines(
% 0.85/1.26 orthogonal_through_point( skol3, skol1 ), orthogonal_through_point( skol3
% 0.85/1.26 , skol2 ) ) }.
% 0.85/1.26 substitution0:
% 0.85/1.26 end
% 0.85/1.26 permutation0:
% 0.85/1.26 0 ==> 0
% 0.85/1.26 end
% 0.85/1.26
% 0.85/1.26 resolution: (2633) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 0.85/1.26 distinct_lines( X, Y ) }.
% 0.85/1.26 parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.85/1.26 parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 0.85/1.26 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 0.85/1.26 substitution0:
% 0.85/1.26 X := X
% 0.85/1.26 end
% 0.85/1.26 substitution1:
% 0.85/1.26 X := X
% 0.85/1.26 Y := Y
% 0.85/1.26 Z := X
% 0.85/1.26 end
% 0.85/1.26
% 0.85/1.26 subsumption: (55) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 0.85/1.26 distinct_lines( X, Y ) }.
% 0.85/1.26 parent0: (2633) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 0.85/1.26 distinct_lines( X, Y ) }.
% 0.85/1.26 substitution0:
% 0.85/1.26 X := Y
% 0.85/1.26 Y := X
% 0.85/1.26 end
% 0.85/1.26 permutation0:
% 0.85/1.26 0 ==> 1
% 0.85/1.26 1 ==> 0
% 0.85/1.26 end
% 0.85/1.26
% 0.85/1.26 resolution: (2635) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 0.85/1.26 convergent_lines( X, Y ) }.
% 0.85/1.26 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.85/1.26 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 0.85/1.26 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.85/1.26 substitution0:
% 0.85/1.26 X := X
% 0.85/1.26 end
% 0.85/1.26 substitution1:
% 0.85/1.26 X := X
% 0.85/1.26 Y := Y
% 0.85/1.26 Z := X
% 0.85/1.26 end
% 0.85/1.26
% 0.85/1.26 subsumption: (63) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.85/1.26 convergent_lines( X, Y ) }.
% 0.85/1.26 parent0: (2635) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 0.85/1.26 convergent_lines( X, Y ) }.
% 0.85/1.26 substitution0:
% 0.85/1.26 X := Y
% 0.85/1.26 Y := X
% 0.85/1.26 end
% 0.85/1.26 permutation0:
% 0.85/1.26 0 ==> 1
% 0.85/1.26 1 ==> 0
% 0.85/1.26 end
% 0.85/1.26
% 0.85/1.26 resolution: (2637) {G1,W5,D3,L1,V2,M1} { convergent_lines(
% 0.85/1.26 orthogonal_through_point( X, Y ), X ) }.
% 0.85/1.26 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 0.85/1.26 orthogonal_through_point( Y, X ), Y ) }.
% 0.85/1.26 parent1[1]: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 0.85/1.26 unorthogonal_lines( X, Y ) }.
% 0.85/1.26 substitution0:
% 0.85/1.26 X := Y
% 0.85/1.26 Y := X
% 0.85/1.26 end
% 0.85/1.26 substitution1:
% 0.85/1.26 X := orthogonal_through_point( X, Y )
% 0.85/1.26 Y := X
% 0.85/1.26 end
% 0.85/1.26
% 0.85/1.26 subsumption: (71) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 0.85/1.26 orthogonal_through_point( X, Y ), X ) }.
% 0.85/1.26 parent0: (2637) {G1,W5,D3,L1,V2,M1} { convergent_lines(
% 0.85/1.26 orthogonal_through_point( X, Y ), X ) }.
% 0.85/1.26 substitution0:
% 0.85/1.26 X := X
% 0.85/1.26 Y := Y
% 0.85/1.26 end
% 0.85/1.26 permutation0:
% 0.85/1.26 0 ==> 0
% 0.85/1.26 end
% 0.85/1.26
% 0.85/1.26 resolution: (2638) {G1,W8,D3,L2,V3,M2} { convergent_lines(
% 0.85/1.26 orthogonal_through_point( X, Y ), Z ), convergent_lines( X, Z ) }.
% 0.85/1.26 parent0[2]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 0.85/1.26 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.85/1.26 parent1[0]: (71) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 0.85/1.26 orthogonal_through_point( X, Y ), X ) }.
% 0.85/1.26 substitution0:
% 0.85/1.26 X := orthogonal_through_point( X, Y )
% 0.85/1.26 Y := X
% 0.85/1.26 Z := Z
% 0.85/1.26 end
% 0.85/1.26 substitution1:
% 0.85/1.26 X := X
% 0.85/1.26 Y := Y
% 0.85/1.26 end
% 0.85/1.26
% 0.85/1.26 subsumption: (73) {G2,W8,D3,L2,V3,M2} R(71,5) { convergent_lines( X, Z ),
% 0.85/1.26 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.85/1.26 parent0: (2638) {G1,W8,D3,L2,V3,M2} { convergent_lines(
% 0.85/1.26 orthogonal_through_point( X, Y ), Z ), convergent_lines( X, Z ) }.
% 0.85/1.26 substitution0:
% 0.85/1.26 X := X
% 0.85/1.26 Y := Y
% 0.85/1.26 Z := Z
% 0.85/1.26 end
% 0.85/1.26 permutation0:
% 0.85/1.26 0 ==> 1
% 0.85/1.26 1 ==> 0
% 0.85/1.26 end
% 0.85/1.26
% 0.85/1.26 resolution: (2639) {G1,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), !
% 0.85/1.26 distinct_lines( Y, X ) }.
% 0.85/1.26 parent0[1]: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 0.85/1.26 distinct_lines( X, Y ) }.
% 0.85/1.26 parent1[1]: (55) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 0.85/1.26 distinct_lines( X, Y ) }.
% 0.85/1.26 substitution0:
% 0.85/1.26 X := X
% 0.85/1.26 Y := Y
% 0.85/1.26 end
% 0.85/1.26 substitution1:
% 0.85/1.26 X := X
% 0.85/1.26 Y := Y
% 0.85/1.26 end
% 0.85/1.26
% 0.85/1.26 subsumption: (74) {G2,W6,D2,L2,V2,M1} R(14,55) { convergent_lines( X, Y ),
% 0.85/1.26 ! distinct_lines( Y, X ) }.
% 0.85/1.26 parent0: (2639) {G1,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), !
% 0.85/1.26 distinct_lines( Y, X ) }.
% 0.85/1.26 substitution0:
% 0.85/1.26 X := X
% 0.85/1.26 Y := Y
% 0.85/1.26 end
% 0.85/1.26 permutation0:
% 0.85/1.26 0 ==> 0
% 0.85/1.26 1 ==> 1
% 0.85/1.26 end
% 0.85/1.26
% 0.85/1.26 resolution: (2640) {G1,W7,D3,L1,V0,M1} { distinct_lines(
% 0.85/1.26 orthogonal_through_point( skol3, skol1 ), orthogonal_through_point( skol3
% 0.85/1.26 , skol2 ) ) }.
% 0.85/1.26 parent0[0]: (47) {G0,W7,D3,L1,V0,M1} I { ! equal_lines(
% 0.85/1.26 orthogonal_through_point( skol3, skol1 ), orthogonal_through_point( skol3
% 0.85/1.26 , skol2 ) ) }.
% 0.85/1.26 parent1[1]: (39) {G0,W6,D2,L2,V2,M1} I { distinct_lines( X, Y ),
% 0.85/1.26 equal_lines( X, Y ) }.
% 0.85/1.26 substitution0:
% 0.85/1.26 end
% 0.85/1.26 substitution1:
% 0.85/1.26 X := orthogonal_through_point( skol3, skol1 )
% 0.85/1.26 Y := orthogonal_through_point( skol3, skol2 )
% 0.85/1.26 end
% 0.85/1.26
% 0.85/1.26 subsumption: (105) {G1,W7,D3,L1,V0,M1} R(47,39) { distinct_lines(
% 0.85/1.26 orthogonal_through_point( skol3, skol1 ), orthogonal_through_point( skol3
% 0.85/1.26 , skol2 ) ) }.
% 0.85/1.26 parent0: (2640) {G1,W7,D3,L1,V0,M1} { distinct_lines(
% 0.85/1.26 orthogonal_through_point( skol3, skol1 ), orthogonal_through_point( skol3
% 0.85/1.26 , skol2 ) ) }.
% 0.85/1.26 substitution0:
% 0.85/1.26 end
% 0.85/1.26 permutation0:
% 0.85/1.26 0 ==> 0
% 0.85/1.26 end
% 0.85/1.26
% 0.85/1.26 resolution: (2641) {G2,W7,D3,L1,V0,M1} { convergent_lines(
% 0.85/1.26 orthogonal_through_point( skol3, skol2 ), orthogonal_through_point( skol3
% 0.85/1.26 , skol1 ) ) }.
% 0.85/1.26 parent0[1]: (74) {G2,W6,D2,L2,V2,M1} R(14,55) { convergent_lines( X, Y ), !
% 0.85/1.26 distinct_lines( Y, X ) }.
% 0.85/1.26 parent1[0]: (105) {G1,W7,D3,L1,V0,M1} R(47,39) { distinct_lines(
% 0.85/1.26 orthogonal_through_point( skol3, skol1 ), orthogonal_through_point( skol3
% 0.85/1.26 , skol2 ) ) }.
% 0.85/1.26 substitution0:
% 0.85/1.26 X := orthogonal_through_point( skol3, skol2 )
% 0.85/1.26 Y := orthogonal_through_point( skol3, skol1 )
% 0.85/1.26 end
% 0.85/1.26 substitution1:
% 0.85/1.26 end
% 0.85/1.26
% 0.85/1.26 subsumption: (106) {G3,W7,D3,L1,V0,M1} R(105,74) { convergent_lines(
% 0.85/1.26 orthogonal_through_point( skol3, skol2 ), orthogonal_through_point( skol3
% 0.85/1.26 , skol1 ) ) }.
% 0.85/1.26 parent0: (2641) {G2,W7,D3,L1,V0,M1} { convergent_lines(
% 0.85/1.26 orthogonal_through_point( skol3, skol2 ), orthogonal_through_point( skol3
% 0.85/1.26 , skol1 ) ) }.
% 0.85/1.26 substitution0:
% 0.85/1.26 end
% 0.85/1.26 permutation0:
% 0.85/1.26 0 ==> 0
% 0.85/1.26 end
% 0.85/1.26
% 0.85/1.26 resolution: (2642) {G1,W10,D3,L2,V1,M2} { convergent_lines(
% 0.85/1.26 orthogonal_through_point( skol3, skol2 ), X ), convergent_lines(
% 0.85/1.26 orthogonal_through_point( skol3, skol1 ), X ) }.
% 0.85/1.26 parent0[2]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 0.85/1.26 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.85/1.26 parent1[0]: (106) {G3,W7,D3,L1,V0,M1} R(105,74) { convergent_lines(
% 0.85/1.26 orthogonal_through_point( skol3, skol2 ), orthogonal_through_point( skol3
% 0.85/1.26 , skol1 ) ) }.
% 0.85/1.26 substitution0:
% 0.85/1.26 X := orthogonal_through_point( skol3, skol2 )
% 0.85/1.26 Y := orthogonal_through_point( skol3, skol1 )
% 0.85/1.26 Z := X
% 0.85/1.26 end
% 0.85/1.26 substitution1:
% 0.85/1.26 end
% 0.85/1.26
% 0.85/1.26 subsumption: (110) {G4,W10,D3,L2,V1,M1} R(106,5) { convergent_lines(
% 0.85/1.26 orthogonal_through_point( skol3, skol1 ), X ), convergent_lines(
% 0.85/1.27 orthogonal_through_point( skol3, skol2 ), X ) }.
% 0.85/1.27 parent0: (2642) {G1,W10,D3,L2,V1,M2} { convergent_lines(
% 0.85/1.27 orthogonal_through_point( skol3, skol2 ), X ), convergent_lines(
% 0.85/1.27 orthogonal_through_point( skol3, skol1 ), X ) }.
% 0.85/1.27 substitution0:
% 0.85/1.27 X := X
% 0.85/1.27 end
% 0.85/1.27 permutation0:
% 0.85/1.27 0 ==> 1
% 0.85/1.27 1 ==> 0
% 0.85/1.27 end
% 0.85/1.27
% 0.85/1.27 resolution: (2643) {G2,W8,D3,L2,V3,M2} { convergent_lines( Y, X ),
% 0.85/1.27 convergent_lines( orthogonal_through_point( X, Z ), Y ) }.
% 0.85/1.27 parent0[0]: (63) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.85/1.27 convergent_lines( X, Y ) }.
% 0.85/1.27 parent1[0]: (73) {G2,W8,D3,L2,V3,M2} R(71,5) { convergent_lines( X, Z ),
% 0.85/1.27 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.85/1.27 substitution0:
% 0.85/1.27 X := Y
% 0.85/1.27 Y := X
% 0.85/1.27 end
% 0.85/1.27 substitution1:
% 0.85/1.27 X := X
% 0.85/1.27 Y := Z
% 0.85/1.27 Z := Y
% 0.85/1.27 end
% 0.85/1.27
% 0.85/1.27 subsumption: (144) {G3,W8,D3,L2,V3,M2} R(73,63) { convergent_lines( Z, X )
% 0.85/1.27 , convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.85/1.27 parent0: (2643) {G2,W8,D3,L2,V3,M2} { convergent_lines( Y, X ),
% 0.85/1.27 convergent_lines( orthogonal_through_point( X, Z ), Y ) }.
% 0.85/1.27 substitution0:
% 0.85/1.27 X := X
% 0.85/1.27 Y := Z
% 0.85/1.27 Z := Y
% 0.85/1.27 end
% 0.85/1.27 permutation0:
% 0.85/1.27 0 ==> 0
% 0.85/1.27 1 ==> 1
% 0.85/1.27 end
% 0.85/1.27
% 0.85/1.27 resolution: (2646) {G2,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 0.85/1.27 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ) }.
% 0.85/1.27 parent0[0]: (63) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.85/1.27 convergent_lines( X, Y ) }.
% 0.85/1.27 parent1[1]: (144) {G3,W8,D3,L2,V3,M2} R(73,63) { convergent_lines( Z, X ),
% 0.85/1.27 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.85/1.27 substitution0:
% 0.85/1.27 X := Z
% 0.85/1.27 Y := orthogonal_through_point( X, Y )
% 0.85/1.27 end
% 0.85/1.27 substitution1:
% 0.85/1.27 X := X
% 0.85/1.27 Y := Y
% 0.85/1.27 Z := Z
% 0.85/1.27 end
% 0.85/1.27
% 0.85/1.27 subsumption: (158) {G4,W8,D3,L2,V3,M2} R(144,63) { convergent_lines( X,
% 0.85/1.27 orthogonal_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 0.85/1.27 parent0: (2646) {G2,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 0.85/1.27 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ) }.
% 0.85/1.27 substitution0:
% 0.85/1.27 X := Y
% 0.85/1.27 Y := Z
% 0.85/1.27 Z := X
% 0.85/1.27 end
% 0.85/1.27 permutation0:
% 0.85/1.27 0 ==> 0
% 0.85/1.27 1 ==> 1
% 0.85/1.27 end
% 0.85/1.27
% 0.85/1.27 resolution: (2648) {G1,W12,D2,L4,V3,M4} { convergent_lines( X, Y ), !
% 0.85/1.27 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ),
% 0.85/1.27 unorthogonal_lines( Z, Y ) }.
% 0.85/1.27 parent0[1]: (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! alpha1
% 0.85/1.27 ( X, Y ) }.
% 0.85/1.27 parent1[3]: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 0.85/1.27 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 0.85/1.27 }.
% 0.85/1.27 substitution0:
% 0.85/1.27 X := X
% 0.85/1.27 Y := Y
% 0.85/1.27 end
% 0.85/1.27 substitution1:
% 0.85/1.27 X := X
% 0.85/1.27 Y := Z
% 0.85/1.27 Z := Y
% 0.85/1.27 end
% 0.85/1.27
% 0.85/1.27 subsumption: (161) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y
% 0.85/1.27 ), convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 0.85/1.27 unorthogonal_lines( Y, Z ) }.
% 0.85/1.27 parent0: (2648) {G1,W12,D2,L4,V3,M4} { convergent_lines( X, Y ), !
% 0.85/1.27 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ),
% 0.85/1.27 unorthogonal_lines( Z, Y ) }.
% 0.85/1.27 substitution0:
% 0.85/1.27 X := X
% 0.85/1.27 Y := Z
% 0.85/1.27 Z := Y
% 0.85/1.27 end
% 0.85/1.27 permutation0:
% 0.85/1.27 0 ==> 1
% 0.85/1.27 1 ==> 0
% 0.85/1.27 2 ==> 2
% 0.85/1.27 3 ==> 3
% 0.85/1.27 end
% 0.85/1.27
% 0.85/1.27 resolution: (2650) {G1,W8,D3,L2,V3,M2} { ! convergent_lines( Z, X ),
% 0.85/1.27 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.85/1.27 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 0.85/1.27 orthogonal_through_point( Y, X ), Y ) }.
% 0.85/1.27 parent1[2]: (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ),
% 0.85/1.27 unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ) }.
% 0.85/1.27 substitution0:
% 0.85/1.27 X := Y
% 0.85/1.27 Y := X
% 0.85/1.27 end
% 0.85/1.27 substitution1:
% 0.85/1.27 X := Z
% 0.85/1.27 Y := X
% 0.85/1.27 Z := orthogonal_through_point( X, Y )
% 0.85/1.27 end
% 0.85/1.27
% 0.85/1.27 subsumption: (305) {G1,W8,D3,L2,V3,M1} R(31,23) { ! convergent_lines( X, Y
% 0.85/1.27 ), unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 0.85/1.27 parent0: (2650) {G1,W8,D3,L2,V3,M2} { ! convergent_lines( Z, X ),
% 0.85/1.27 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.85/1.27 substitution0:
% 0.85/1.27 X := Y
% 0.85/1.27 Y := Z
% 0.85/1.27 Z := X
% 0.85/1.27 end
% 0.85/1.27 permutation0:
% 0.85/1.27 0 ==> 0
% 0.85/1.27 1 ==> 1
% 0.85/1.27 end
% 0.85/1.27
% 0.85/1.27 resolution: (2651) {G1,W13,D3,L3,V3,M3} { ! convergent_lines( Z,
% 0.85/1.27 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ), !
% 0.85/1.27 unorthogonal_lines( Z, orthogonal_through_point( X, Y ) ) }.
% 0.85/1.27 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 0.85/1.27 orthogonal_through_point( Y, X ), Y ) }.
% 0.85/1.27 parent1[3]: (161) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y
% 0.85/1.27 ), convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 0.85/1.27 unorthogonal_lines( Y, Z ) }.
% 0.85/1.27 substitution0:
% 0.85/1.27 X := Y
% 0.85/1.27 Y := X
% 0.85/1.27 end
% 0.85/1.27 substitution1:
% 0.85/1.27 X := Z
% 0.85/1.27 Y := orthogonal_through_point( X, Y )
% 0.85/1.27 Z := X
% 0.85/1.27 end
% 0.85/1.27
% 0.85/1.27 resolution: (2652) {G2,W11,D3,L3,V3,M3} { convergent_lines( X, Y ), !
% 0.85/1.27 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ),
% 0.85/1.27 convergent_lines( X, Y ) }.
% 0.85/1.27 parent0[0]: (2651) {G1,W13,D3,L3,V3,M3} { ! convergent_lines( Z,
% 0.85/1.27 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ), !
% 0.85/1.27 unorthogonal_lines( Z, orthogonal_through_point( X, Y ) ) }.
% 0.85/1.27 parent1[0]: (158) {G4,W8,D3,L2,V3,M2} R(144,63) { convergent_lines( X,
% 0.85/1.27 orthogonal_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 0.85/1.27 substitution0:
% 0.85/1.27 X := Y
% 0.85/1.27 Y := Z
% 0.85/1.27 Z := X
% 0.85/1.27 end
% 0.85/1.27 substitution1:
% 0.85/1.27 X := X
% 0.85/1.27 Y := Y
% 0.85/1.27 Z := Z
% 0.85/1.27 end
% 0.85/1.27
% 0.85/1.27 factor: (2653) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 0.85/1.27 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 0.85/1.27 parent0[0, 2]: (2652) {G2,W11,D3,L3,V3,M3} { convergent_lines( X, Y ), !
% 0.85/1.27 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ),
% 0.85/1.27 convergent_lines( X, Y ) }.
% 0.85/1.27 substitution0:
% 0.85/1.27 X := X
% 0.85/1.27 Y := Y
% 0.85/1.27 Z := Z
% 0.85/1.27 end
% 0.85/1.27
% 0.85/1.27 subsumption: (2148) {G5,W8,D3,L2,V3,M1} R(161,23);r(158) { convergent_lines
% 0.85/1.27 ( X, Y ), ! unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 0.85/1.27 parent0: (2653) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 0.85/1.27 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 0.85/1.27 substitution0:
% 0.85/1.27 X := X
% 0.85/1.27 Y := Y
% 0.85/1.27 Z := Z
% 0.85/1.27 end
% 0.85/1.27 permutation0:
% 0.85/1.27 0 ==> 0
% 0.85/1.27 1 ==> 1
% 0.85/1.27 end
% 0.85/1.27
% 0.85/1.27 resolution: (2654) {G2,W10,D3,L2,V4,M2} { convergent_lines(
% 0.85/1.27 orthogonal_through_point( X, Y ), Z ), ! convergent_lines(
% 0.85/1.27 orthogonal_through_point( Z, T ), X ) }.
% 0.85/1.27 parent0[1]: (2148) {G5,W8,D3,L2,V3,M1} R(161,23);r(158) { convergent_lines
% 0.85/1.27 ( X, Y ), ! unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 0.85/1.27 parent1[1]: (305) {G1,W8,D3,L2,V3,M1} R(31,23) { ! convergent_lines( X, Y )
% 0.85/1.27 , unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 0.85/1.27 substitution0:
% 0.85/1.27 X := orthogonal_through_point( X, Y )
% 0.85/1.27 Y := Z
% 0.85/1.27 Z := T
% 0.85/1.27 end
% 0.85/1.27 substitution1:
% 0.85/1.27 X := orthogonal_through_point( Z, T )
% 0.85/1.27 Y := X
% 0.85/1.27 Z := Y
% 0.85/1.27 end
% 0.85/1.27
% 0.85/1.27 subsumption: (2155) {G6,W10,D3,L2,V4,M2} R(2148,305) { ! convergent_lines(
% 0.85/1.27 orthogonal_through_point( Z, T ), X ), convergent_lines(
% 0.85/1.27 orthogonal_through_point( X, Y ), Z ) }.
% 0.85/1.27 parent0: (2654) {G2,W10,D3,L2,V4,M2} { convergent_lines(
% 0.85/1.27 orthogonal_through_point( X, Y ), Z ), ! convergent_lines(
% 0.85/1.27 orthogonal_through_point( Z, T ), X ) }.
% 0.85/1.27 substitution0:
% 0.85/1.27 X := X
% 0.85/1.27 Y := Y
% 0.85/1.27 Z := Z
% 0.85/1.27 T := T
% 0.85/1.27 end
% 0.85/1.27 permutation0:
% 0.85/1.27 0 ==> 1
% 0.85/1.27 1 ==> 0
% 0.85/1.27 end
% 0.85/1.27
% 0.85/1.27 resolution: (2655) {G1,W7,D4,L1,V3,M1} { ! convergent_lines(
% 0.85/1.27 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 0.85/1.27 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.85/1.27 parent1[1]: (2155) {G6,W10,D3,L2,V4,M2} R(2148,305) { ! convergent_lines(
% 0.85/1.27 orthogonal_through_point( Z, T ), X ), convergent_lines(
% 0.85/1.27 orthogonal_through_point( X, Y ), Z ) }.
% 0.85/1.27 substitution0:
% 0.85/1.27 X := orthogonal_through_point( X, Y )
% 0.85/1.27 end
% 0.85/1.27 substitution1:
% 0.85/1.27 X := X
% 0.85/1.27 Y := Y
% 0.85/1.27 Z := orthogonal_through_point( X, Y )
% 0.85/1.27 T := Z
% 0.85/1.27 end
% 0.85/1.27
% 0.85/1.27 subsumption: (2334) {G7,W7,D4,L1,V3,M1} R(2155,2) { ! convergent_lines(
% 0.85/1.27 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 0.85/1.27 parent0: (2655) {G1,W7,D4,L1,V3,M1} { ! convergent_lines(
% 0.85/1.27 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 0.85/1.27 substitution0:
% 0.85/1.27 X := X
% 0.85/1.27 Y := Y
% 0.85/1.27 Z := Z
% 0.85/1.27 end
% 0.85/1.27 permutation0:
% 0.85/1.27 0 ==> 0
% 0.85/1.27 end
% 0.85/1.27
% 0.85/1.27 resolution: (2656) {G7,W7,D3,L1,V3,M1} { ! convergent_lines(
% 0.85/1.27 orthogonal_through_point( X, T ), orthogonal_through_point( X, Y ) ) }.
% 0.85/1.27 parent0[0]: (2334) {G7,W7,D4,L1,V3,M1} R(2155,2) { ! convergent_lines(
% 0.85/1.27 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 0.85/1.27 parent1[1]: (2155) {G6,W10,D3,L2,V4,M2} R(2148,305) { ! convergent_lines(
% 0.85/1.27 orthogonal_through_point( Z, T ), X ), convergent_lines(
% 0.85/1.27 orthogonal_through_point( X, Y ), Z ) }.
% 0.85/1.27 substitution0:
% 0.85/1.27 X := X
% 0.85/1.27 Y := Y
% 0.85/1.27 Z := Z
% 0.85/1.27 end
% 0.85/1.27 substitution1:
% 0.85/1.27 X := orthogonal_through_point( X, Y )
% 0.85/1.27 Y := Z
% 0.85/1.27 Z := X
% 0.85/1.27 T := T
% 0.85/1.27 end
% 0.85/1.27
% 0.85/1.27 subsumption: (2337) {G8,W7,D3,L1,V3,M1} R(2334,2155) { ! convergent_lines(
% 0.85/1.27 orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ) }.
% 0.85/1.27 parent0: (2656) {G7,W7,D3,L1,V3,M1} { ! convergent_lines(
% 0.85/1.27 orthogonal_through_point( X, T ), orthogonal_through_point( X, Y ) ) }.
% 0.85/1.27 substitution0:
% 0.85/1.27 X := X
% 0.85/1.27 Y := Z
% 0.85/1.27 Z := T
% 0.85/1.27 T := Y
% 0.85/1.27 end
% 0.85/1.27 permutation0:
% 0.85/1.27 0 ==> 0
% 0.85/1.27 end
% 0.85/1.27
% 0.85/1.27 resolution: (2657) {G5,W7,D3,L1,V1,M1} { convergent_lines(
% 0.85/1.27 orthogonal_through_point( skol3, skol2 ), orthogonal_through_point( skol3
% 0.85/1.27 , X ) ) }.
% 0.85/1.27 parent0[0]: (2337) {G8,W7,D3,L1,V3,M1} R(2334,2155) { ! convergent_lines(
% 0.85/1.27 orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ) }.
% 0.85/1.27 parent1[0]: (110) {G4,W10,D3,L2,V1,M1} R(106,5) { convergent_lines(
% 0.85/1.27 orthogonal_through_point( skol3, skol1 ), X ), convergent_lines(
% 0.85/1.27 orthogonal_through_point( skol3, skol2 ), X ) }.
% 0.85/1.27 substitution0:
% 0.85/1.27 X := skol3
% 0.85/1.27 Y := skol1
% 0.85/1.27 Z := X
% 0.85/1.27 end
% 0.85/1.27 substitution1:
% 0.85/1.27 X := orthogonal_through_point( skol3, X )
% 0.85/1.27 end
% 0.85/1.27
% 0.85/1.27 resolution: (2659) {G6,W0,D0,L0,V0,M0} { }.
% 0.85/1.27 parent0[0]: (2337) {G8,W7,D3,L1,V3,M1} R(2334,2155) { ! convergent_lines(
% 0.85/1.27 orthogonal_through_point( X, Y ), orthogonal_through_point( X, Z ) ) }.
% 0.85/1.27 parent1[0]: (2657) {G5,W7,D3,L1,V1,M1} { convergent_lines(
% 0.85/1.27 orthogonal_through_point( skol3, skol2 ), orthogonal_through_point( skol3
% 0.85/1.27 , X ) ) }.
% 0.85/1.27 substitution0:
% 0.85/1.27 X := skol3
% 0.85/1.27 Y := skol2
% 0.85/1.27 Z := X
% 0.85/1.27 end
% 0.85/1.27 substitution1:
% 0.85/1.27 X := X
% 0.85/1.27 end
% 0.85/1.27
% 0.85/1.27 subsumption: (2484) {G9,W0,D0,L0,V0,M0} R(2337,110);r(2337) { }.
% 0.85/1.27 parent0: (2659) {G6,W0,D0,L0,V0,M0} { }.
% 0.85/1.27 substitution0:
% 0.85/1.27 end
% 0.85/1.27 permutation0:
% 0.85/1.27 end
% 0.85/1.27
% 0.85/1.27 Proof check complete!
% 0.85/1.27
% 0.85/1.27 Memory use:
% 0.85/1.27
% 0.85/1.27 space for terms: 35908
% 0.85/1.27 space for clauses: 102082
% 0.85/1.27
% 0.85/1.27
% 0.85/1.27 clauses generated: 26495
% 0.85/1.27 clauses kept: 2485
% 0.85/1.27 clauses selected: 369
% 0.85/1.27 clauses deleted: 3
% 0.85/1.27 clauses inuse deleted: 2
% 0.85/1.27
% 0.85/1.27 subsentry: 513986
% 0.85/1.27 literals s-matched: 239718
% 0.85/1.27 literals matched: 239656
% 0.85/1.27 full subsumption: 162358
% 0.85/1.27
% 0.85/1.27 checksum: 361324551
% 0.85/1.27
% 0.85/1.27
% 0.85/1.27 Bliksem ended
%------------------------------------------------------------------------------