TSTP Solution File: GEO225+3 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO225+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n026.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 02:53:01 EDT 2022
% Result : Theorem 0.73s 1.13s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO225+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Sat Jun 18 10:48:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.73/1.13 *** allocated 10000 integers for termspace/termends
% 0.73/1.13 *** allocated 10000 integers for clauses
% 0.73/1.13 *** allocated 10000 integers for justifications
% 0.73/1.13 Bliksem 1.12
% 0.73/1.13
% 0.73/1.13
% 0.73/1.13 Automatic Strategy Selection
% 0.73/1.13
% 0.73/1.13
% 0.73/1.13 Clauses:
% 0.73/1.13
% 0.73/1.13 { ! distinct_points( X, X ) }.
% 0.73/1.13 { ! distinct_lines( X, X ) }.
% 0.73/1.13 { ! convergent_lines( X, X ) }.
% 0.73/1.13 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 0.73/1.13 ) }.
% 0.73/1.13 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.73/1.13 }.
% 0.73/1.13 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 0.73/1.13 , Z ) }.
% 0.73/1.13 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 0.73/1.13 , Y ) ) }.
% 0.73/1.13 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 0.73/1.13 , Y ) ) }.
% 0.73/1.13 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.73/1.13 , Y ), X ) }.
% 0.73/1.13 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.73/1.13 , Y ), Y ) }.
% 0.73/1.13 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 0.73/1.13 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 0.73/1.13 apart_point_and_line( Y, T ) }.
% 0.73/1.13 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 0.73/1.13 apart_point_and_line( Z, Y ) }.
% 0.73/1.13 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 0.73/1.13 apart_point_and_line( X, Z ) }.
% 0.73/1.13 { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X,
% 0.73/1.13 Z ) }.
% 0.73/1.13 { ! distinct_lines( X, Y ), convergent_lines( X, Y ) }.
% 0.73/1.13 { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 0.73/1.13 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 0.73/1.13 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 0.73/1.13 apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 0.73/1.13 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.73/1.13 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.73/1.13 , convergent_lines( Y, Z ) }.
% 0.73/1.13 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.73/1.13 , unorthogonal_lines( Y, Z ) }.
% 0.73/1.13 { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 0.73/1.13 { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.73/1.13 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 0.73/1.13 }.
% 0.73/1.13 { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 0.73/1.13 { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 0.73/1.13 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 0.73/1.13 apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ),
% 0.73/1.13 unorthogonal_lines( Y, T ) }.
% 0.73/1.13 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.73/1.13 { alpha2( X, Z ), convergent_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 0.73/1.13 unorthogonal_lines( X, Y ) }.
% 0.73/1.13 { alpha2( X, Z ), unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 0.73/1.13 unorthogonal_lines( X, Y ) }.
% 0.73/1.13 { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 0.73/1.13 { ! alpha2( X, Y ), unorthogonal_lines( Y, X ) }.
% 0.73/1.13 { ! convergent_lines( Y, X ), ! unorthogonal_lines( Y, X ), alpha2( X, Y )
% 0.73/1.13 }.
% 0.73/1.13 { unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ), !
% 0.73/1.13 convergent_lines( X, Y ) }.
% 0.73/1.13 { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line(
% 0.73/1.13 line_connecting( X, Y ) ) }.
% 0.73/1.13 { ! line( X ), ! line( Y ), ! convergent_lines( X, Y ), point(
% 0.73/1.13 intersection_point( X, Y ) ) }.
% 0.73/1.13 { ! line( X ), ! point( Y ), line( parallel_through_point( X, Y ) ) }.
% 0.73/1.13 { ! line( X ), ! point( Y ), line( orthogonal_through_point( X, Y ) ) }.
% 0.73/1.13 { ! equal_points( X, Y ), ! distinct_points( X, Y ) }.
% 0.73/1.13 { distinct_points( X, Y ), equal_points( X, Y ) }.
% 0.73/1.13 { ! equal_lines( X, Y ), ! distinct_lines( X, Y ) }.
% 0.73/1.13 { distinct_lines( X, Y ), equal_lines( X, Y ) }.
% 0.73/1.13 { ! parallel_lines( X, Y ), ! convergent_lines( X, Y ) }.
% 0.73/1.13 { convergent_lines( X, Y ), parallel_lines( X, Y ) }.
% 0.73/1.13 { ! incident_point_and_line( X, Y ), ! apart_point_and_line( X, Y ) }.
% 0.73/1.13 { apart_point_and_line( X, Y ), incident_point_and_line( X, Y ) }.
% 0.73/1.13 { ! orthogonal_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.73/1.13 { unorthogonal_lines( X, Y ), orthogonal_lines( X, Y ) }.
% 0.73/1.13 { point( skol1 ) }.
% 0.73/1.13 { point( skol2 ) }.
% 0.73/1.13 { distinct_points( skol1, skol2 ) }.
% 0.73/1.13 { line( X ) }.
% 0.73/1.13 { ! incident_point_and_line( skol1, X ), ! incident_point_and_line( skol2,
% 0.73/1.13 X ) }.
% 0.73/1.13
% 0.73/1.13 percentage equality = 0.000000, percentage horn = 0.627451
% 0.73/1.13 This a non-horn, non-equality problem
% 0.73/1.13
% 0.73/1.13
% 0.73/1.13 Options Used:
% 0.73/1.13
% 0.73/1.13 useres = 1
% 0.73/1.13 useparamod = 0
% 0.73/1.13 useeqrefl = 0
% 0.73/1.13 useeqfact = 0
% 0.73/1.13 usefactor = 1
% 0.73/1.13 usesimpsplitting = 0
% 0.73/1.13 usesimpdemod = 0
% 0.73/1.13 usesimpres = 3
% 0.73/1.13
% 0.73/1.13 resimpinuse = 1000
% 0.73/1.13 resimpclauses = 20000
% 0.73/1.13 substype = standard
% 0.73/1.13 backwardsubs = 1
% 0.73/1.13 selectoldest = 5
% 0.73/1.13
% 0.73/1.13 litorderings [0] = split
% 0.73/1.13 litorderings [1] = liftord
% 0.73/1.13
% 0.73/1.13 termordering = none
% 0.73/1.13
% 0.73/1.13 litapriori = 1
% 0.73/1.13 termapriori = 0
% 0.73/1.13 litaposteriori = 0
% 0.73/1.13 termaposteriori = 0
% 0.73/1.13 demodaposteriori = 0
% 0.73/1.13 ordereqreflfact = 0
% 0.73/1.13
% 0.73/1.13 litselect = none
% 0.73/1.13
% 0.73/1.13 maxweight = 15
% 0.73/1.13 maxdepth = 30000
% 0.73/1.13 maxlength = 115
% 0.73/1.13 maxnrvars = 195
% 0.73/1.13 excuselevel = 1
% 0.73/1.13 increasemaxweight = 1
% 0.73/1.13
% 0.73/1.13 maxselected = 10000000
% 0.73/1.13 maxnrclauses = 10000000
% 0.73/1.13
% 0.73/1.13 showgenerated = 0
% 0.73/1.13 showkept = 0
% 0.73/1.13 showselected = 0
% 0.73/1.13 showdeleted = 0
% 0.73/1.13 showresimp = 1
% 0.73/1.13 showstatus = 2000
% 0.73/1.13
% 0.73/1.13 prologoutput = 0
% 0.73/1.13 nrgoals = 5000000
% 0.73/1.13 totalproof = 1
% 0.73/1.13
% 0.73/1.13 Symbols occurring in the translation:
% 0.73/1.13
% 0.73/1.13 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.73/1.13 . [1, 2] (w:1, o:25, a:1, s:1, b:0),
% 0.73/1.13 ! [4, 1] (w:0, o:18, a:1, s:1, b:0),
% 0.73/1.13 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.73/1.13 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.73/1.13 distinct_points [36, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.73/1.13 distinct_lines [37, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.73/1.13 convergent_lines [38, 2] (w:1, o:49, a:1, s:1, b:0),
% 0.73/1.13 line_connecting [41, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.73/1.13 apart_point_and_line [42, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.73/1.13 intersection_point [43, 2] (w:1, o:54, a:1, s:1, b:0),
% 0.73/1.13 parallel_through_point [46, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.73/1.13 unorthogonal_lines [49, 2] (w:1, o:58, a:1, s:1, b:0),
% 0.73/1.13 orthogonal_through_point [52, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.73/1.13 point [54, 1] (w:1, o:23, a:1, s:1, b:0),
% 0.73/1.13 line [55, 1] (w:1, o:24, a:1, s:1, b:0),
% 0.73/1.13 equal_points [56, 2] (w:1, o:59, a:1, s:1, b:0),
% 0.73/1.13 equal_lines [57, 2] (w:1, o:60, a:1, s:1, b:0),
% 0.73/1.13 parallel_lines [58, 2] (w:1, o:61, a:1, s:1, b:0),
% 0.73/1.13 incident_point_and_line [59, 2] (w:1, o:62, a:1, s:1, b:0),
% 0.73/1.13 orthogonal_lines [60, 2] (w:1, o:56, a:1, s:1, b:0),
% 0.73/1.13 alpha1 [61, 2] (w:1, o:63, a:1, s:1, b:0),
% 0.73/1.13 alpha2 [62, 2] (w:1, o:64, a:1, s:1, b:0),
% 0.73/1.13 skol1 [63, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.73/1.13 skol2 [64, 0] (w:1, o:17, a:1, s:1, b:0).
% 0.73/1.13
% 0.73/1.13
% 0.73/1.13 Starting Search:
% 0.73/1.13
% 0.73/1.13
% 0.73/1.13 Bliksems!, er is een bewijs:
% 0.73/1.13 % SZS status Theorem
% 0.73/1.13 % SZS output start Refutation
% 0.73/1.13
% 0.73/1.13 (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.73/1.13 (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.73/1.13 , ! distinct_lines( X, Y ) }.
% 0.73/1.13 (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), apart_point_and_line(
% 0.73/1.13 X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.73/1.13 (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! distinct_lines( X
% 0.73/1.13 , Y ) }.
% 0.73/1.13 (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines( parallel_through_point( Y
% 0.73/1.13 , X ), Y ) }.
% 0.73/1.13 (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.73/1.13 parallel_through_point( Y, X ) ) }.
% 0.73/1.13 (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.73/1.13 orthogonal_through_point( Y, X ) ) }.
% 0.73/1.13 (43) {G0,W6,D2,L2,V2,M1} I { apart_point_and_line( X, Y ),
% 0.73/1.13 incident_point_and_line( X, Y ) }.
% 0.73/1.13 (50) {G0,W6,D2,L2,V1,M1} I { ! incident_point_and_line( skol1, X ), !
% 0.73/1.13 incident_point_and_line( skol2, X ) }.
% 0.73/1.13 (61) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 0.73/1.13 ( X, Y ) }.
% 0.73/1.13 (78) {G2,W6,D2,L2,V2,M1} R(14,61) { convergent_lines( X, Y ), !
% 0.73/1.13 distinct_lines( Y, X ) }.
% 0.73/1.13 (116) {G1,W6,D2,L2,V1,M1} R(50,43) { apart_point_and_line( skol2, X ), !
% 0.73/1.13 incident_point_and_line( skol1, X ) }.
% 0.73/1.13 (128) {G2,W6,D2,L2,V1,M1} R(116,43) { apart_point_and_line( skol1, X ),
% 0.73/1.13 apart_point_and_line( skol2, X ) }.
% 0.73/1.13 (133) {G3,W5,D3,L1,V1,M1} R(128,24) { apart_point_and_line( skol1,
% 0.73/1.13 orthogonal_through_point( X, skol2 ) ) }.
% 0.73/1.13 (149) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X,
% 0.73/1.13 parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.73/1.13 (152) {G4,W7,D3,L1,V2,M1} R(149,133) { distinct_lines(
% 0.73/1.13 orthogonal_through_point( X, skol2 ), parallel_through_point( Y, skol1 )
% 0.73/1.13 ) }.
% 0.73/1.13 (156) {G5,W7,D3,L1,V2,M1} R(152,78) { convergent_lines(
% 0.73/1.13 parallel_through_point( X, skol1 ), orthogonal_through_point( Y, skol2 )
% 0.73/1.13 ) }.
% 0.73/1.13 (161) {G6,W0,D0,L0,V0,M0} R(156,15) { }.
% 0.73/1.13
% 0.73/1.13
% 0.73/1.13 % SZS output end Refutation
% 0.73/1.13 found a proof!
% 0.73/1.13
% 0.73/1.13
% 0.73/1.13 Unprocessed initial clauses:
% 0.73/1.13
% 0.73/1.13 (163) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 0.73/1.13 (164) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.73/1.13 (165) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 0.73/1.13 (166) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 0.73/1.13 , Z ), distinct_points( Y, Z ) }.
% 0.73/1.13 (167) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X, Z
% 0.73/1.13 ), distinct_lines( Y, Z ) }.
% 0.73/1.13 (168) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines(
% 0.73/1.13 X, Z ), convergent_lines( Y, Z ) }.
% 0.73/1.13 (169) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.73/1.13 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 0.73/1.13 (170) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.73/1.13 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 0.73/1.13 (171) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 0.73/1.13 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 0.73/1.13 (172) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 0.73/1.13 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 0.73/1.13 (173) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines(
% 0.73/1.13 Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 0.73/1.13 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 0.73/1.13 (174) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 0.73/1.13 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 0.73/1.13 (175) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ), distinct_lines
% 0.73/1.13 ( Y, Z ), apart_point_and_line( X, Z ) }.
% 0.73/1.13 (176) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), distinct_lines( Y
% 0.73/1.13 , Z ), convergent_lines( X, Z ) }.
% 0.73/1.13 (177) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ), convergent_lines( X
% 0.73/1.13 , Y ) }.
% 0.73/1.13 (178) {G0,W5,D3,L1,V2,M1} { ! convergent_lines( parallel_through_point( Y
% 0.73/1.13 , X ), Y ) }.
% 0.73/1.13 (179) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.73/1.13 parallel_through_point( Y, X ) ) }.
% 0.73/1.13 (180) {G0,W12,D2,L4,V3,M4} { ! distinct_lines( X, Y ),
% 0.73/1.13 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 0.73/1.13 convergent_lines( X, Y ) }.
% 0.73/1.13 (181) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines(
% 0.73/1.13 X, Y ) }.
% 0.73/1.13 (182) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.73/1.13 unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 0.73/1.13 (183) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.73/1.13 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 0.73/1.13 }.
% 0.73/1.13 (184) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 0.73/1.13 (185) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 0.73/1.13 }.
% 0.73/1.13 (186) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( X, Y ), !
% 0.73/1.13 unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 0.73/1.13 (187) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines( orthogonal_through_point
% 0.73/1.13 ( Y, X ), Y ) }.
% 0.73/1.13 (188) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.73/1.13 orthogonal_through_point( Y, X ) ) }.
% 0.73/1.13 (189) {G0,W15,D2,L5,V4,M5} { ! distinct_lines( X, Y ),
% 0.73/1.13 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 0.73/1.13 unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 0.73/1.13 (190) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines(
% 0.73/1.13 X, Y ) }.
% 0.73/1.13 (191) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), convergent_lines( Z, Y ), !
% 0.73/1.13 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.73/1.13 (192) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), unorthogonal_lines( Z, Y ), !
% 0.73/1.13 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.73/1.13 (193) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 0.73/1.13 (194) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), unorthogonal_lines( Y, X )
% 0.73/1.13 }.
% 0.73/1.13 (195) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( Y, X ), !
% 0.73/1.13 unorthogonal_lines( Y, X ), alpha2( X, Y ) }.
% 0.73/1.13 (196) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ), unorthogonal_lines
% 0.73/1.13 ( Z, Y ), ! convergent_lines( X, Y ) }.
% 0.73/1.13 (197) {G0,W11,D3,L4,V2,M4} { ! point( X ), ! point( Y ), ! distinct_points
% 0.73/1.13 ( X, Y ), line( line_connecting( X, Y ) ) }.
% 0.73/1.13 (198) {G0,W11,D3,L4,V2,M4} { ! line( X ), ! line( Y ), ! convergent_lines
% 0.73/1.13 ( X, Y ), point( intersection_point( X, Y ) ) }.
% 0.73/1.13 (199) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 0.73/1.13 parallel_through_point( X, Y ) ) }.
% 0.73/1.13 (200) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 0.73/1.13 orthogonal_through_point( X, Y ) ) }.
% 0.73/1.13 (201) {G0,W6,D2,L2,V2,M2} { ! equal_points( X, Y ), ! distinct_points( X,
% 0.73/1.13 Y ) }.
% 0.73/1.13 (202) {G0,W6,D2,L2,V2,M2} { distinct_points( X, Y ), equal_points( X, Y )
% 0.73/1.13 }.
% 0.73/1.13 (203) {G0,W6,D2,L2,V2,M2} { ! equal_lines( X, Y ), ! distinct_lines( X, Y
% 0.73/1.13 ) }.
% 0.73/1.13 (204) {G0,W6,D2,L2,V2,M2} { distinct_lines( X, Y ), equal_lines( X, Y )
% 0.73/1.13 }.
% 0.73/1.13 (205) {G0,W6,D2,L2,V2,M2} { ! parallel_lines( X, Y ), ! convergent_lines(
% 0.73/1.13 X, Y ) }.
% 0.73/1.13 (206) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), parallel_lines( X, Y
% 0.73/1.13 ) }.
% 0.73/1.13 (207) {G0,W6,D2,L2,V2,M2} { ! incident_point_and_line( X, Y ), !
% 0.73/1.13 apart_point_and_line( X, Y ) }.
% 0.73/1.13 (208) {G0,W6,D2,L2,V2,M2} { apart_point_and_line( X, Y ),
% 0.73/1.13 incident_point_and_line( X, Y ) }.
% 0.73/1.13 (209) {G0,W6,D2,L2,V2,M2} { ! orthogonal_lines( X, Y ), !
% 0.73/1.13 unorthogonal_lines( X, Y ) }.
% 0.73/1.13 (210) {G0,W6,D2,L2,V2,M2} { unorthogonal_lines( X, Y ), orthogonal_lines(
% 0.73/1.13 X, Y ) }.
% 0.73/1.13 (211) {G0,W2,D2,L1,V0,M1} { point( skol1 ) }.
% 0.73/1.13 (212) {G0,W2,D2,L1,V0,M1} { point( skol2 ) }.
% 0.73/1.13 (213) {G0,W3,D2,L1,V0,M1} { distinct_points( skol1, skol2 ) }.
% 0.73/1.13 (214) {G0,W2,D2,L1,V1,M1} { line( X ) }.
% 0.73/1.13 (215) {G0,W6,D2,L2,V1,M2} { ! incident_point_and_line( skol1, X ), !
% 0.73/1.13 incident_point_and_line( skol2, X ) }.
% 0.73/1.13
% 0.73/1.13
% 0.73/1.13 Total Proof:
% 0.73/1.13
% 0.73/1.13 subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.73/1.13 parent0: (164) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.73/1.13 substitution0:
% 0.73/1.13 X := X
% 0.73/1.13 end
% 0.73/1.13 permutation0:
% 0.73/1.13 0 ==> 0
% 0.73/1.13 end
% 0.73/1.13
% 0.73/1.13 subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 0.73/1.13 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 0.73/1.13 parent0: (167) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ),
% 0.73/1.13 distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 0.73/1.13 substitution0:
% 0.73/1.13 X := X
% 0.73/1.13 Y := Y
% 0.73/1.13 Z := Z
% 0.73/1.13 end
% 0.73/1.13 permutation0:
% 0.73/1.13 0 ==> 2
% 0.73/1.13 1 ==> 0
% 0.73/1.13 2 ==> 1
% 0.73/1.13 end
% 0.73/1.13
% 0.73/1.13 subsumption: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 0.73/1.13 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.73/1.13 parent0: (175) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 0.73/1.13 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 0.73/1.13 substitution0:
% 0.73/1.13 X := X
% 0.73/1.13 Y := Y
% 0.73/1.13 Z := Z
% 0.73/1.13 end
% 0.73/1.13 permutation0:
% 0.73/1.13 0 ==> 2
% 0.73/1.13 1 ==> 0
% 0.73/1.13 2 ==> 1
% 0.73/1.13 end
% 0.73/1.13
% 0.73/1.13 subsumption: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 0.73/1.13 distinct_lines( X, Y ) }.
% 0.73/1.13 parent0: (177) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ),
% 0.73/1.13 convergent_lines( X, Y ) }.
% 0.73/1.13 substitution0:
% 0.73/1.13 X := X
% 0.73/1.13 Y := Y
% 0.73/1.13 end
% 0.73/1.13 permutation0:
% 0.73/1.13 0 ==> 1
% 0.73/1.13 1 ==> 0
% 0.73/1.13 end
% 0.73/1.13
% 0.73/1.13 subsumption: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 0.73/1.13 parallel_through_point( Y, X ), Y ) }.
% 0.73/1.13 parent0: (178) {G0,W5,D3,L1,V2,M1} { ! convergent_lines(
% 0.73/1.13 parallel_through_point( Y, X ), Y ) }.
% 0.73/1.13 substitution0:
% 0.73/1.13 X := X
% 0.73/1.13 Y := Y
% 0.73/1.13 end
% 0.73/1.13 permutation0:
% 0.73/1.13 0 ==> 0
% 0.73/1.13 end
% 0.73/1.13
% 0.73/1.13 subsumption: (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.73/1.13 parallel_through_point( Y, X ) ) }.
% 0.73/1.13 parent0: (179) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.73/1.13 parallel_through_point( Y, X ) ) }.
% 0.73/1.13 substitution0:
% 0.73/1.13 X := X
% 0.73/1.13 Y := Y
% 0.73/1.13 end
% 0.73/1.13 permutation0:
% 0.73/1.13 0 ==> 0
% 0.73/1.13 end
% 0.73/1.13
% 0.73/1.13 subsumption: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.73/1.13 orthogonal_through_point( Y, X ) ) }.
% 0.73/1.13 parent0: (188) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.73/1.13 orthogonal_through_point( Y, X ) ) }.
% 0.73/1.13 substitution0:
% 0.73/1.13 X := X
% 0.73/1.13 Y := Y
% 0.73/1.13 end
% 0.73/1.13 permutation0:
% 0.73/1.13 0 ==> 0
% 0.73/1.13 end
% 0.73/1.13
% 0.73/1.13 *** allocated 15000 integers for clauses
% 0.73/1.13 subsumption: (43) {G0,W6,D2,L2,V2,M1} I { apart_point_and_line( X, Y ),
% 0.73/1.13 incident_point_and_line( X, Y ) }.
% 0.73/1.13 parent0: (208) {G0,W6,D2,L2,V2,M2} { apart_point_and_line( X, Y ),
% 0.73/1.13 incident_point_and_line( X, Y ) }.
% 0.73/1.13 substitution0:
% 0.73/1.13 X := X
% 0.73/1.13 Y := Y
% 0.73/1.13 end
% 0.73/1.13 permutation0:
% 0.73/1.13 0 ==> 0
% 0.73/1.13 1 ==> 1
% 0.73/1.13 end
% 0.73/1.13
% 0.73/1.13 subsumption: (50) {G0,W6,D2,L2,V1,M1} I { ! incident_point_and_line( skol1
% 0.73/1.13 , X ), ! incident_point_and_line( skol2, X ) }.
% 0.73/1.13 parent0: (215) {G0,W6,D2,L2,V1,M2} { ! incident_point_and_line( skol1, X )
% 0.73/1.13 , ! incident_point_and_line( skol2, X ) }.
% 0.73/1.13 substitution0:
% 0.73/1.13 X := X
% 0.73/1.13 end
% 0.73/1.13 permutation0:
% 0.73/1.13 0 ==> 0
% 0.73/1.13 1 ==> 1
% 0.73/1.13 end
% 0.73/1.13
% 0.73/1.13 resolution: (294) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 0.73/1.13 distinct_lines( X, Y ) }.
% 0.73/1.13 parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.73/1.13 parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 0.73/1.13 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 0.73/1.13 substitution0:
% 0.73/1.13 X := X
% 0.73/1.13 end
% 0.73/1.13 substitution1:
% 0.73/1.13 X := X
% 0.73/1.13 Y := Y
% 0.73/1.13 Z := X
% 0.73/1.13 end
% 0.73/1.13
% 0.73/1.13 subsumption: (61) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 0.73/1.13 distinct_lines( X, Y ) }.
% 0.73/1.13 parent0: (294) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 0.73/1.13 distinct_lines( X, Y ) }.
% 0.73/1.13 substitution0:
% 0.73/1.13 X := Y
% 0.73/1.13 Y := X
% 0.73/1.13 end
% 0.73/1.13 permutation0:
% 0.73/1.13 0 ==> 1
% 0.73/1.13 1 ==> 0
% 0.73/1.13 end
% 0.73/1.13
% 0.73/1.13 resolution: (296) {G1,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), !
% 0.73/1.13 distinct_lines( Y, X ) }.
% 0.73/1.13 parent0[1]: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 0.73/1.13 distinct_lines( X, Y ) }.
% 0.73/1.13 parent1[1]: (61) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 0.73/1.13 distinct_lines( X, Y ) }.
% 0.73/1.13 substitution0:
% 0.73/1.13 X := X
% 0.73/1.13 Y := Y
% 0.73/1.13 end
% 0.73/1.13 substitution1:
% 0.73/1.13 X := X
% 0.73/1.13 Y := Y
% 0.73/1.13 end
% 0.73/1.13
% 0.73/1.13 subsumption: (78) {G2,W6,D2,L2,V2,M1} R(14,61) { convergent_lines( X, Y ),
% 0.73/1.13 ! distinct_lines( Y, X ) }.
% 0.73/1.13 parent0: (296) {G1,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), !
% 0.73/1.13 distinct_lines( Y, X ) }.
% 0.73/1.13 substitution0:
% 0.73/1.13 X := X
% 0.73/1.13 Y := Y
% 0.73/1.13 end
% 0.73/1.13 permutation0:
% 0.73/1.13 0 ==> 0
% 0.73/1.13 1 ==> 1
% 0.73/1.13 end
% 0.73/1.13
% 0.73/1.13 resolution: (298) {G1,W6,D2,L2,V1,M2} { ! incident_point_and_line( skol1,
% 0.73/1.13 X ), apart_point_and_line( skol2, X ) }.
% 0.73/1.13 parent0[1]: (50) {G0,W6,D2,L2,V1,M1} I { ! incident_point_and_line( skol1,
% 0.73/1.13 X ), ! incident_point_and_line( skol2, X ) }.
% 0.73/1.13 parent1[1]: (43) {G0,W6,D2,L2,V2,M1} I { apart_point_and_line( X, Y ),
% 0.73/1.13 incident_point_and_line( X, Y ) }.
% 0.73/1.13 substitution0:
% 0.73/1.13 X := X
% 0.73/1.13 end
% 0.73/1.13 substitution1:
% 0.73/1.13 X := skol2
% 0.73/1.13 Y := X
% 0.73/1.13 end
% 0.73/1.13
% 0.73/1.13 subsumption: (116) {G1,W6,D2,L2,V1,M1} R(50,43) { apart_point_and_line(
% 0.73/1.13 skol2, X ), ! incident_point_and_line( skol1, X ) }.
% 0.73/1.13 parent0: (298) {G1,W6,D2,L2,V1,M2} { ! incident_point_and_line( skol1, X )
% 0.73/1.13 , apart_point_and_line( skol2, X ) }.
% 0.73/1.13 substitution0:
% 0.73/1.13 X := X
% 0.73/1.13 end
% 0.73/1.13 permutation0:
% 0.73/1.13 0 ==> 1
% 0.73/1.13 1 ==> 0
% 0.73/1.13 end
% 0.73/1.13
% 0.73/1.13 resolution: (299) {G1,W6,D2,L2,V1,M2} { apart_point_and_line( skol2, X ),
% 0.73/1.13 apart_point_and_line( skol1, X ) }.
% 0.73/1.13 parent0[1]: (116) {G1,W6,D2,L2,V1,M1} R(50,43) { apart_point_and_line(
% 0.73/1.13 skol2, X ), ! incident_point_and_line( skol1, X ) }.
% 0.73/1.13 parent1[1]: (43) {G0,W6,D2,L2,V2,M1} I { apart_point_and_line( X, Y ),
% 0.73/1.13 incident_point_and_line( X, Y ) }.
% 0.73/1.13 substitution0:
% 0.73/1.13 X := X
% 0.73/1.13 end
% 0.73/1.13 substitution1:
% 0.73/1.13 X := skol1
% 0.73/1.13 Y := X
% 0.73/1.13 end
% 0.73/1.13
% 0.73/1.13 subsumption: (128) {G2,W6,D2,L2,V1,M1} R(116,43) { apart_point_and_line(
% 0.73/1.13 skol1, X ), apart_point_and_line( skol2, X ) }.
% 0.73/1.13 parent0: (299) {G1,W6,D2,L2,V1,M2} { apart_point_and_line( skol2, X ),
% 0.73/1.13 apart_point_and_line( skol1, X ) }.
% 0.73/1.13 substitution0:
% 0.73/1.13 X := X
% 0.73/1.13 end
% 0.73/1.13 permutation0:
% 0.73/1.13 0 ==> 1
% 0.73/1.13 1 ==> 0
% 0.73/1.13 end
% 0.73/1.13
% 0.73/1.13 resolution: (301) {G1,W5,D3,L1,V1,M1} { apart_point_and_line( skol1,
% 0.73/1.13 orthogonal_through_point( X, skol2 ) ) }.
% 0.73/1.13 parent0[0]: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.73/1.13 orthogonal_through_point( Y, X ) ) }.
% 0.73/1.13 parent1[1]: (128) {G2,W6,D2,L2,V1,M1} R(116,43) { apart_point_and_line(
% 0.73/1.13 skol1, X ), apart_point_and_line( skol2, X ) }.
% 0.73/1.13 substitution0:
% 0.73/1.13 X := skol2
% 0.73/1.13 Y := X
% 0.73/1.13 end
% 0.73/1.13 substitution1:
% 0.73/1.13 X := orthogonal_through_point( X, skol2 )
% 0.73/1.13 end
% 0.73/1.13
% 0.73/1.13 subsumption: (133) {G3,W5,D3,L1,V1,M1} R(128,24) { apart_point_and_line(
% 0.73/1.13 skol1, orthogonal_through_point( X, skol2 ) ) }.
% 0.73/1.13 parent0: (301) {G1,W5,D3,L1,V1,M1} { apart_point_and_line( skol1,
% 0.73/1.13 orthogonal_through_point( X, skol2 ) ) }.
% 0.73/1.13 substitution0:
% 0.73/1.13 X := X
% 0.73/1.13 end
% 0.73/1.13 permutation0:
% 0.73/1.13 0 ==> 0
% 0.73/1.13 end
% 0.73/1.13
% 0.73/1.13 resolution: (302) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 0.73/1.13 parallel_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 0.73/1.13 parent0[0]: (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.73/1.13 parallel_through_point( Y, X ) ) }.
% 0.73/1.13 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 0.73/1.13 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.73/1.13 substitution0:
% 0.73/1.13 X := X
% 0.73/1.13 Y := Y
% 0.73/1.13 end
% 0.73/1.13 substitution1:
% 0.73/1.13 X := X
% 0.73/1.13 Y := Z
% 0.73/1.13 Z := parallel_through_point( Y, X )
% 0.73/1.13 end
% 0.73/1.13
% 0.73/1.13 subsumption: (149) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X,
% 0.73/1.13 parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.73/1.13 parent0: (302) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 0.73/1.13 parallel_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 0.73/1.13 substitution0:
% 0.73/1.13 X := Z
% 0.73/1.13 Y := Y
% 0.73/1.13 Z := X
% 0.73/1.13 end
% 0.73/1.13 permutation0:
% 0.73/1.13 0 ==> 0
% 0.73/1.13 1 ==> 1
% 0.73/1.13 end
% 0.73/1.13
% 0.73/1.13 resolution: (303) {G2,W7,D3,L1,V2,M1} { distinct_lines(
% 0.73/1.13 orthogonal_through_point( X, skol2 ), parallel_through_point( Y, skol1 )
% 0.73/1.13 ) }.
% 0.73/1.13 parent0[1]: (149) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X,
% 0.73/1.13 parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.73/1.13 parent1[0]: (133) {G3,W5,D3,L1,V1,M1} R(128,24) { apart_point_and_line(
% 0.73/1.13 skol1, orthogonal_through_point( X, skol2 ) ) }.
% 0.73/1.13 substitution0:
% 0.73/1.13 X := orthogonal_through_point( X, skol2 )
% 0.73/1.13 Y := Y
% 0.73/1.13 Z := skol1
% 0.73/1.13 end
% 0.73/1.13 substitution1:
% 0.73/1.13 X := X
% 0.73/1.13 end
% 0.73/1.13
% 0.73/1.13 subsumption: (152) {G4,W7,D3,L1,V2,M1} R(149,133) { distinct_lines(
% 0.73/1.13 orthogonal_through_point( X, skol2 ), parallel_through_point( Y, skol1 )
% 0.73/1.13 ) }.
% 0.73/1.13 parent0: (303) {G2,W7,D3,L1,V2,M1} { distinct_lines(
% 0.73/1.13 orthogonal_through_point( X, skol2 ), parallel_through_point( Y, skol1 )
% 0.73/1.13 ) }.
% 0.73/1.13 substitution0:
% 0.73/1.13 X := X
% 0.73/1.13 Y := Y
% 0.73/1.13 end
% 0.73/1.13 permutation0:
% 0.73/1.13 0 ==> 0
% 0.73/1.13 end
% 0.73/1.13
% 0.73/1.13 resolution: (304) {G3,W7,D3,L1,V2,M1} { convergent_lines(
% 0.73/1.13 parallel_through_point( X, skol1 ), orthogonal_through_point( Y, skol2 )
% 0.73/1.13 ) }.
% 0.73/1.13 parent0[1]: (78) {G2,W6,D2,L2,V2,M1} R(14,61) { convergent_lines( X, Y ), !
% 0.73/1.13 distinct_lines( Y, X ) }.
% 0.73/1.13 parent1[0]: (152) {G4,W7,D3,L1,V2,M1} R(149,133) { distinct_lines(
% 0.73/1.13 orthogonal_through_point( X, skol2 ), parallel_through_point( Y, skol1 )
% 0.73/1.13 ) }.
% 0.73/1.13 substitution0:
% 0.73/1.13 X := parallel_through_point( X, skol1 )
% 0.73/1.13 Y := orthogonal_through_point( Y, skol2 )
% 0.73/1.13 end
% 0.73/1.13 substitution1:
% 0.73/1.13 X := Y
% 0.73/1.13 Y := X
% 0.73/1.13 end
% 0.73/1.13
% 0.73/1.13 subsumption: (156) {G5,W7,D3,L1,V2,M1} R(152,78) { convergent_lines(
% 0.73/1.13 parallel_through_point( X, skol1 ), orthogonal_through_point( Y, skol2 )
% 0.73/1.13 ) }.
% 0.73/1.13 parent0: (304) {G3,W7,D3,L1,V2,M1} { convergent_lines(
% 0.73/1.13 parallel_through_point( X, skol1 ), orthogonal_through_point( Y, skol2 )
% 0.73/1.13 ) }.
% 0.73/1.13 substitution0:
% 0.73/1.13 X := X
% 0.73/1.13 Y := Y
% 0.73/1.13 end
% 0.73/1.13 permutation0:
% 0.73/1.13 0 ==> 0
% 0.73/1.13 end
% 0.73/1.13
% 0.73/1.13 resolution: (305) {G1,W0,D0,L0,V0,M0} { }.
% 0.73/1.13 parent0[0]: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 0.73/1.13 parallel_through_point( Y, X ), Y ) }.
% 0.73/1.13 parent1[0]: (156) {G5,W7,D3,L1,V2,M1} R(152,78) { convergent_lines(
% 0.73/1.13 parallel_through_point( X, skol1 ), orthogonal_through_point( Y, skol2 )
% 0.73/1.13 ) }.
% 0.73/1.13 substitution0:
% 0.73/1.13 X := skol1
% 0.73/1.13 Y := orthogonal_through_point( X, skol2 )
% 0.73/1.13 end
% 0.73/1.13 substitution1:
% 0.73/1.13 X := orthogonal_through_point( X, skol2 )
% 0.73/1.13 Y := X
% 0.73/1.13 end
% 0.73/1.13
% 0.73/1.13 subsumption: (161) {G6,W0,D0,L0,V0,M0} R(156,15) { }.
% 0.73/1.13 parent0: (305) {G1,W0,D0,L0,V0,M0} { }.
% 0.73/1.13 substitution0:
% 0.73/1.13 end
% 0.73/1.13 permutation0:
% 0.73/1.13 end
% 0.73/1.13
% 0.73/1.13 Proof check complete!
% 0.73/1.13
% 0.73/1.13 Memory use:
% 0.73/1.13
% 0.73/1.13 space for terms: 3120
% 0.73/1.13 space for clauses: 7662
% 0.73/1.13
% 0.73/1.13
% 0.73/1.13 clauses generated: 396
% 0.73/1.13 clauses kept: 162
% 0.73/1.13 clauses selected: 59
% 0.73/1.13 clauses deleted: 0
% 0.73/1.13 clauses inuse deleted: 0
% 0.73/1.13
% 0.73/1.13 subsentry: 625
% 0.73/1.13 literals s-matched: 500
% 0.73/1.13 literals matched: 465
% 0.73/1.13 full subsumption: 149
% 0.73/1.13
% 0.73/1.13 checksum: 1789938515
% 0.73/1.13
% 0.73/1.13
% 0.73/1.13 Bliksem ended
%------------------------------------------------------------------------------