%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO209+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n019.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 02:52:46 EDT 2022
% Result : Theorem 0.78s 1.18s
% Output : Refutation 0.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GEO209+3 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.14 % Command : bliksem %s
% 0.13/0.36 % Computer : n019.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % DateTime : Sat Jun 18 15:38:09 EDT 2022
% 0.13/0.36 % CPUTime :
% 0.78/1.17 *** allocated 10000 integers for termspace/termends
% 0.78/1.17 *** allocated 10000 integers for clauses
% 0.78/1.17 *** allocated 10000 integers for justifications
% 0.78/1.17 Bliksem 1.12
% 0.78/1.17
% 0.78/1.17
% 0.78/1.17 Automatic Strategy Selection
% 0.78/1.17
% 0.78/1.17
% 0.78/1.17 Clauses:
% 0.78/1.17
% 0.78/1.17 { ! distinct_points( X, X ) }.
% 0.78/1.17 { ! distinct_lines( X, X ) }.
% 0.78/1.17 { ! convergent_lines( X, X ) }.
% 0.78/1.17 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 0.78/1.17 ) }.
% 0.78/1.17 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.78/1.17 }.
% 0.78/1.17 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 0.78/1.17 , Z ) }.
% 0.78/1.17 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 0.78/1.17 , Y ) ) }.
% 0.78/1.17 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 0.78/1.17 , Y ) ) }.
% 0.78/1.17 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.78/1.17 , Y ), X ) }.
% 0.78/1.17 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.78/1.17 , Y ), Y ) }.
% 0.78/1.17 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 0.78/1.17 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 0.78/1.17 apart_point_and_line( Y, T ) }.
% 0.78/1.17 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 0.78/1.17 apart_point_and_line( Z, Y ) }.
% 0.78/1.17 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 0.78/1.17 apart_point_and_line( X, Z ) }.
% 0.78/1.17 { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X,
% 0.78/1.17 Z ) }.
% 0.78/1.17 { ! distinct_lines( X, Y ), convergent_lines( X, Y ) }.
% 0.78/1.17 { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 0.78/1.17 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 0.78/1.17 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 0.78/1.17 apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 0.78/1.17 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.78/1.17 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.78/1.17 , convergent_lines( Y, Z ) }.
% 0.78/1.17 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.78/1.17 , unorthogonal_lines( Y, Z ) }.
% 0.78/1.17 { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 0.78/1.17 { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.78/1.17 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 0.78/1.17 }.
% 0.78/1.17 { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 0.78/1.17 { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 0.78/1.17 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 0.78/1.17 apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ),
% 0.78/1.17 unorthogonal_lines( Y, T ) }.
% 0.78/1.17 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.78/1.17 { alpha2( X, Z ), convergent_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 0.78/1.17 unorthogonal_lines( X, Y ) }.
% 0.78/1.17 { alpha2( X, Z ), unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 0.78/1.17 unorthogonal_lines( X, Y ) }.
% 0.78/1.17 { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 0.78/1.17 { ! alpha2( X, Y ), unorthogonal_lines( Y, X ) }.
% 0.78/1.17 { ! convergent_lines( Y, X ), ! unorthogonal_lines( Y, X ), alpha2( X, Y )
% 0.78/1.17 }.
% 0.78/1.17 { unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ), !
% 0.78/1.17 convergent_lines( X, Y ) }.
% 0.78/1.17 { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line(
% 0.78/1.17 line_connecting( X, Y ) ) }.
% 0.78/1.17 { ! line( X ), ! line( Y ), ! convergent_lines( X, Y ), point(
% 0.78/1.17 intersection_point( X, Y ) ) }.
% 0.78/1.17 { ! line( X ), ! point( Y ), line( parallel_through_point( X, Y ) ) }.
% 0.78/1.17 { ! line( X ), ! point( Y ), line( orthogonal_through_point( X, Y ) ) }.
% 0.78/1.17 { ! equal_points( X, Y ), ! distinct_points( X, Y ) }.
% 0.78/1.17 { distinct_points( X, Y ), equal_points( X, Y ) }.
% 0.78/1.17 { ! equal_lines( X, Y ), ! distinct_lines( X, Y ) }.
% 0.78/1.17 { distinct_lines( X, Y ), equal_lines( X, Y ) }.
% 0.78/1.17 { ! parallel_lines( X, Y ), ! convergent_lines( X, Y ) }.
% 0.78/1.17 { convergent_lines( X, Y ), parallel_lines( X, Y ) }.
% 0.78/1.17 { ! incident_point_and_line( X, Y ), ! apart_point_and_line( X, Y ) }.
% 0.78/1.17 { apart_point_and_line( X, Y ), incident_point_and_line( X, Y ) }.
% 0.78/1.17 { ! orthogonal_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.78/1.17 { unorthogonal_lines( X, Y ), orthogonal_lines( X, Y ) }.
% 0.78/1.17 { apart_point_and_line( skol3, skol4 ) }.
% 0.78/1.17 { incident_point_and_line( skol3, skol1 ) }.
% 0.78/1.17 { incident_point_and_line( skol3, skol2 ) }.
% 0.78/1.17 { parallel_lines( skol1, skol4 ) }.
% 0.78/1.17 { parallel_lines( skol2, skol4 ) }.
% 0.78/1.17 { ! equal_lines( skol1, skol2 ) }.
% 0.78/1.17
% 0.78/1.17 percentage equality = 0.000000, percentage horn = 0.634615
% 0.78/1.17 This a non-horn, non-equality problem
% 0.78/1.17
% 0.78/1.17
% 0.78/1.17 Options Used:
% 0.78/1.17
% 0.78/1.17 useres = 1
% 0.78/1.17 useparamod = 0
% 0.78/1.17 useeqrefl = 0
% 0.78/1.17 useeqfact = 0
% 0.78/1.17 usefactor = 1
% 0.78/1.17 usesimpsplitting = 0
% 0.78/1.17 usesimpdemod = 0
% 0.78/1.17 usesimpres = 3
% 0.78/1.17
% 0.78/1.17 resimpinuse = 1000
% 0.78/1.17 resimpclauses = 20000
% 0.78/1.17 substype = standard
% 0.78/1.17 backwardsubs = 1
% 0.78/1.17 selectoldest = 5
% 0.78/1.17
% 0.78/1.17 litorderings [0] = split
% 0.78/1.17 litorderings [1] = liftord
% 0.78/1.17
% 0.78/1.17 termordering = none
% 0.78/1.17
% 0.78/1.17 litapriori = 1
% 0.78/1.17 termapriori = 0
% 0.78/1.17 litaposteriori = 0
% 0.78/1.17 termaposteriori = 0
% 0.78/1.17 demodaposteriori = 0
% 0.78/1.17 ordereqreflfact = 0
% 0.78/1.17
% 0.78/1.17 litselect = none
% 0.78/1.17
% 0.78/1.17 maxweight = 15
% 0.78/1.17 maxdepth = 30000
% 0.78/1.17 maxlength = 115
% 0.78/1.17 maxnrvars = 195
% 0.78/1.17 excuselevel = 1
% 0.78/1.17 increasemaxweight = 1
% 0.78/1.17
% 0.78/1.17 maxselected = 10000000
% 0.78/1.17 maxnrclauses = 10000000
% 0.78/1.17
% 0.78/1.17 showgenerated = 0
% 0.78/1.17 showkept = 0
% 0.78/1.17 showselected = 0
% 0.78/1.17 showdeleted = 0
% 0.78/1.17 showresimp = 1
% 0.78/1.17 showstatus = 2000
% 0.78/1.17
% 0.78/1.17 prologoutput = 0
% 0.78/1.17 nrgoals = 5000000
% 0.78/1.18 totalproof = 1
% 0.78/1.18
% 0.78/1.18 Symbols occurring in the translation:
% 0.78/1.18
% 0.78/1.18 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.78/1.18 . [1, 2] (w:1, o:27, a:1, s:1, b:0),
% 0.78/1.18 ! [4, 1] (w:0, o:20, a:1, s:1, b:0),
% 0.78/1.18 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.78/1.18 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.78/1.18 distinct_points [36, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.78/1.18 distinct_lines [37, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.78/1.18 convergent_lines [38, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.78/1.18 line_connecting [41, 2] (w:1, o:54, a:1, s:1, b:0),
% 0.78/1.18 apart_point_and_line [42, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.78/1.18 intersection_point [43, 2] (w:1, o:56, a:1, s:1, b:0),
% 0.78/1.18 parallel_through_point [46, 2] (w:1, o:59, a:1, s:1, b:0),
% 0.78/1.18 unorthogonal_lines [49, 2] (w:1, o:60, a:1, s:1, b:0),
% 0.78/1.18 orthogonal_through_point [52, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.78/1.18 point [54, 1] (w:1, o:25, a:1, s:1, b:0),
% 0.78/1.18 line [55, 1] (w:1, o:26, a:1, s:1, b:0),
% 0.78/1.18 equal_points [56, 2] (w:1, o:61, a:1, s:1, b:0),
% 0.78/1.18 equal_lines [57, 2] (w:1, o:62, a:1, s:1, b:0),
% 0.78/1.18 parallel_lines [58, 2] (w:1, o:63, a:1, s:1, b:0),
% 0.78/1.18 incident_point_and_line [59, 2] (w:1, o:64, a:1, s:1, b:0),
% 0.78/1.18 orthogonal_lines [60, 2] (w:1, o:58, a:1, s:1, b:0),
% 0.78/1.18 alpha1 [61, 2] (w:1, o:65, a:1, s:1, b:0),
% 0.78/1.18 alpha2 [62, 2] (w:1, o:66, a:1, s:1, b:0),
% 0.78/1.18 skol1 [63, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.78/1.18 skol2 [64, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.78/1.18 skol3 [65, 0] (w:1, o:18, a:1, s:1, b:0),
% 0.78/1.18 skol4 [66, 0] (w:1, o:19, a:1, s:1, b:0).
% 0.78/1.18
% 0.78/1.18
% 0.78/1.18 Starting Search:
% 0.78/1.18
% 0.78/1.18
% 0.78/1.18 Bliksems!, er is een bewijs:
% 0.78/1.18 % SZS status Theorem
% 0.78/1.18 % SZS output start Refutation
% 0.78/1.18
% 0.78/1.18 (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.78/1.18 (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.78/1.18 , ! distinct_lines( X, Y ) }.
% 0.78/1.18 (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), convergent_lines( Y,
% 0.78/1.18 Z ), ! convergent_lines( X, Y ) }.
% 0.78/1.18 (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! distinct_lines( X
% 0.78/1.18 , Y ) }.
% 0.78/1.18 (39) {G0,W6,D2,L2,V2,M1} I { distinct_lines( X, Y ), equal_lines( X, Y )
% 0.78/1.18 }.
% 0.78/1.18 (40) {G0,W6,D2,L2,V2,M1} I { ! convergent_lines( X, Y ), ! parallel_lines(
% 0.78/1.18 X, Y ) }.
% 0.78/1.18 (49) {G0,W3,D2,L1,V0,M1} I { parallel_lines( skol1, skol4 ) }.
% 0.78/1.18 (50) {G0,W3,D2,L1,V0,M1} I { parallel_lines( skol2, skol4 ) }.
% 0.78/1.18 (51) {G0,W3,D2,L1,V0,M1} I { ! equal_lines( skol1, skol2 ) }.
% 0.78/1.18 (57) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 0.78/1.18 ( X, Y ) }.
% 0.78/1.18 (75) {G1,W3,D2,L1,V0,M1} R(40,49) { ! convergent_lines( skol1, skol4 ) }.
% 0.78/1.18 (76) {G1,W3,D2,L1,V0,M1} R(40,50) { ! convergent_lines( skol2, skol4 ) }.
% 0.78/1.18 (87) {G1,W3,D2,L1,V0,M1} R(39,51) { distinct_lines( skol1, skol2 ) }.
% 0.78/1.18 (88) {G2,W3,D2,L1,V0,M1} R(87,57) { distinct_lines( skol2, skol1 ) }.
% 0.78/1.18 (157) {G3,W3,D2,L1,V0,M1} R(14,88) { convergent_lines( skol2, skol1 ) }.
% 0.78/1.18 (164) {G4,W6,D2,L2,V1,M1} R(157,5) { convergent_lines( skol1, X ),
% 0.78/1.18 convergent_lines( skol2, X ) }.
% 0.78/1.18 (167) {G5,W0,D0,L0,V0,M0} R(164,76);r(75) { }.
% 0.78/1.18
% 0.78/1.18
% 0.78/1.18 % SZS output end Refutation
% 0.78/1.18 found a proof!
% 0.78/1.18
% 0.78/1.18
% 0.78/1.18 Unprocessed initial clauses:
% 0.78/1.18
% 0.78/1.18 (169) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 0.78/1.18 (170) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.78/1.18 (171) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 0.78/1.18 (172) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 0.78/1.18 , Z ), distinct_points( Y, Z ) }.
% 0.78/1.18 (173) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X, Z
% 0.78/1.18 ), distinct_lines( Y, Z ) }.
% 0.78/1.18 (174) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines(
% 0.78/1.18 X, Z ), convergent_lines( Y, Z ) }.
% 0.78/1.18 (175) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.78/1.18 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 0.78/1.18 (176) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.78/1.18 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 0.78/1.18 (177) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 0.78/1.18 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 0.78/1.18 (178) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 0.78/1.18 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 0.78/1.18 (179) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines(
% 0.78/1.18 Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 0.78/1.18 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 0.78/1.18 (180) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 0.78/1.18 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 0.78/1.18 (181) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ), distinct_lines
% 0.78/1.18 ( Y, Z ), apart_point_and_line( X, Z ) }.
% 0.78/1.18 (182) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), distinct_lines( Y
% 0.78/1.18 , Z ), convergent_lines( X, Z ) }.
% 0.78/1.18 (183) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ), convergent_lines( X
% 0.78/1.18 , Y ) }.
% 0.78/1.18 (184) {G0,W5,D3,L1,V2,M1} { ! convergent_lines( parallel_through_point( Y
% 0.78/1.18 , X ), Y ) }.
% 0.78/1.18 (185) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.78/1.18 parallel_through_point( Y, X ) ) }.
% 0.78/1.18 (186) {G0,W12,D2,L4,V3,M4} { ! distinct_lines( X, Y ),
% 0.78/1.18 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 0.78/1.18 convergent_lines( X, Y ) }.
% 0.78/1.18 (187) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines(
% 0.78/1.18 X, Y ) }.
% 0.78/1.18 (188) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.78/1.18 unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 0.78/1.18 (189) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.78/1.18 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 0.78/1.18 }.
% 0.78/1.18 (190) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 0.78/1.18 (191) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 0.78/1.18 }.
% 0.78/1.18 (192) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( X, Y ), !
% 0.78/1.18 unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 0.78/1.18 (193) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines( orthogonal_through_point
% 0.78/1.18 ( Y, X ), Y ) }.
% 0.78/1.18 (194) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.78/1.18 orthogonal_through_point( Y, X ) ) }.
% 0.78/1.18 (195) {G0,W15,D2,L5,V4,M5} { ! distinct_lines( X, Y ),
% 0.78/1.18 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 0.78/1.18 unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 0.78/1.18 (196) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines(
% 0.78/1.18 X, Y ) }.
% 0.78/1.18 (197) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), convergent_lines( Z, Y ), !
% 0.78/1.18 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.78/1.18 (198) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), unorthogonal_lines( Z, Y ), !
% 0.78/1.18 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.78/1.18 (199) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 0.78/1.18 (200) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), unorthogonal_lines( Y, X )
% 0.78/1.18 }.
% 0.78/1.18 (201) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( Y, X ), !
% 0.78/1.18 unorthogonal_lines( Y, X ), alpha2( X, Y ) }.
% 0.78/1.18 (202) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ), unorthogonal_lines
% 0.78/1.18 ( Z, Y ), ! convergent_lines( X, Y ) }.
% 0.78/1.18 (203) {G0,W11,D3,L4,V2,M4} { ! point( X ), ! point( Y ), ! distinct_points
% 0.78/1.18 ( X, Y ), line( line_connecting( X, Y ) ) }.
% 0.78/1.18 (204) {G0,W11,D3,L4,V2,M4} { ! line( X ), ! line( Y ), ! convergent_lines
% 0.78/1.18 ( X, Y ), point( intersection_point( X, Y ) ) }.
% 0.78/1.18 (205) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 0.78/1.18 parallel_through_point( X, Y ) ) }.
% 0.78/1.18 (206) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 0.78/1.18 orthogonal_through_point( X, Y ) ) }.
% 0.78/1.18 (207) {G0,W6,D2,L2,V2,M2} { ! equal_points( X, Y ), ! distinct_points( X,
% 0.78/1.18 Y ) }.
% 0.78/1.18 (208) {G0,W6,D2,L2,V2,M2} { distinct_points( X, Y ), equal_points( X, Y )
% 0.78/1.18 }.
% 0.78/1.18 (209) {G0,W6,D2,L2,V2,M2} { ! equal_lines( X, Y ), ! distinct_lines( X, Y
% 0.78/1.18 ) }.
% 0.78/1.18 (210) {G0,W6,D2,L2,V2,M2} { distinct_lines( X, Y ), equal_lines( X, Y )
% 0.78/1.18 }.
% 0.78/1.18 (211) {G0,W6,D2,L2,V2,M2} { ! parallel_lines( X, Y ), ! convergent_lines(
% 0.78/1.18 X, Y ) }.
% 0.78/1.18 (212) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), parallel_lines( X, Y
% 0.78/1.18 ) }.
% 0.78/1.18 (213) {G0,W6,D2,L2,V2,M2} { ! incident_point_and_line( X, Y ), !
% 0.78/1.18 apart_point_and_line( X, Y ) }.
% 0.78/1.18 (214) {G0,W6,D2,L2,V2,M2} { apart_point_and_line( X, Y ),
% 0.78/1.18 incident_point_and_line( X, Y ) }.
% 0.78/1.18 (215) {G0,W6,D2,L2,V2,M2} { ! orthogonal_lines( X, Y ), !
% 0.78/1.18 unorthogonal_lines( X, Y ) }.
% 0.78/1.18 (216) {G0,W6,D2,L2,V2,M2} { unorthogonal_lines( X, Y ), orthogonal_lines(
% 0.78/1.18 X, Y ) }.
% 0.78/1.18 (217) {G0,W3,D2,L1,V0,M1} { apart_point_and_line( skol3, skol4 ) }.
% 0.78/1.18 (218) {G0,W3,D2,L1,V0,M1} { incident_point_and_line( skol3, skol1 ) }.
% 0.78/1.18 (219) {G0,W3,D2,L1,V0,M1} { incident_point_and_line( skol3, skol2 ) }.
% 0.78/1.18 (220) {G0,W3,D2,L1,V0,M1} { parallel_lines( skol1, skol4 ) }.
% 0.78/1.18 (221) {G0,W3,D2,L1,V0,M1} { parallel_lines( skol2, skol4 ) }.
% 0.78/1.18 (222) {G0,W3,D2,L1,V0,M1} { ! equal_lines( skol1, skol2 ) }.
% 0.78/1.18
% 0.78/1.18
% 0.78/1.18 Total Proof:
% 0.78/1.18
% 0.78/1.18 subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.78/1.18 parent0: (170) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.78/1.18 substitution0:
% 0.78/1.18 X := X
% 0.78/1.18 end
% 0.78/1.18 permutation0:
% 0.78/1.18 0 ==> 0
% 0.78/1.18 end
% 0.78/1.18
% 0.78/1.18 subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 0.78/1.18 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 0.78/1.18 parent0: (173) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ),
% 0.78/1.18 distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 0.78/1.18 substitution0:
% 0.78/1.18 X := X
% 0.78/1.18 Y := Y
% 0.78/1.18 Z := Z
% 0.78/1.18 end
% 0.78/1.18 permutation0:
% 0.78/1.18 0 ==> 2
% 0.78/1.18 1 ==> 0
% 0.78/1.18 2 ==> 1
% 0.78/1.18 end
% 0.78/1.18
% 0.78/1.18 subsumption: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 0.78/1.18 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.78/1.18 parent0: (174) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 0.78/1.18 convergent_lines( X, Z ), convergent_lines( Y, Z ) }.
% 0.78/1.18 substitution0:
% 0.78/1.18 X := X
% 0.78/1.18 Y := Y
% 0.78/1.18 Z := Z
% 0.78/1.18 end
% 0.78/1.18 permutation0:
% 0.78/1.18 0 ==> 2
% 0.78/1.18 1 ==> 0
% 0.78/1.18 2 ==> 1
% 0.78/1.18 end
% 0.78/1.18
% 0.78/1.18 subsumption: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 0.78/1.18 distinct_lines( X, Y ) }.
% 0.78/1.18 parent0: (183) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ),
% 0.78/1.18 convergent_lines( X, Y ) }.
% 0.78/1.18 substitution0:
% 0.78/1.18 X := X
% 0.78/1.18 Y := Y
% 0.78/1.18 end
% 0.78/1.18 permutation0:
% 0.78/1.18 0 ==> 1
% 0.78/1.18 1 ==> 0
% 0.78/1.18 end
% 0.78/1.18
% 0.78/1.18 subsumption: (39) {G0,W6,D2,L2,V2,M1} I { distinct_lines( X, Y ),
% 0.78/1.18 equal_lines( X, Y ) }.
% 0.78/1.18 parent0: (210) {G0,W6,D2,L2,V2,M2} { distinct_lines( X, Y ), equal_lines(
% 0.78/1.18 X, Y ) }.
% 0.78/1.18 substitution0:
% 0.78/1.18 X := X
% 0.78/1.18 Y := Y
% 0.78/1.18 end
% 0.78/1.18 permutation0:
% 0.78/1.18 0 ==> 0
% 0.78/1.18 1 ==> 1
% 0.78/1.18 end
% 0.78/1.18
% 0.78/1.18 subsumption: (40) {G0,W6,D2,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 0.78/1.18 parallel_lines( X, Y ) }.
% 0.78/1.18 parent0: (211) {G0,W6,D2,L2,V2,M2} { ! parallel_lines( X, Y ), !
% 0.78/1.18 convergent_lines( X, Y ) }.
% 0.78/1.18 substitution0:
% 0.78/1.18 X := X
% 0.78/1.18 Y := Y
% 0.78/1.18 end
% 0.78/1.18 permutation0:
% 0.78/1.18 0 ==> 1
% 0.78/1.18 1 ==> 0
% 0.78/1.18 end
% 0.78/1.18
% 0.78/1.18 *** allocated 15000 integers for clauses
% 0.78/1.18 subsumption: (49) {G0,W3,D2,L1,V0,M1} I { parallel_lines( skol1, skol4 )
% 0.78/1.18 }.
% 0.78/1.18 parent0: (220) {G0,W3,D2,L1,V0,M1} { parallel_lines( skol1, skol4 ) }.
% 0.78/1.18 substitution0:
% 0.78/1.18 end
% 0.78/1.18 permutation0:
% 0.78/1.18 0 ==> 0
% 0.78/1.18 end
% 0.78/1.18
% 0.78/1.18 subsumption: (50) {G0,W3,D2,L1,V0,M1} I { parallel_lines( skol2, skol4 )
% 0.78/1.18 }.
% 0.78/1.18 parent0: (221) {G0,W3,D2,L1,V0,M1} { parallel_lines( skol2, skol4 ) }.
% 0.78/1.18 substitution0:
% 0.78/1.18 end
% 0.78/1.18 permutation0:
% 0.78/1.18 0 ==> 0
% 0.78/1.18 end
% 0.78/1.18
% 0.78/1.18 subsumption: (51) {G0,W3,D2,L1,V0,M1} I { ! equal_lines( skol1, skol2 ) }.
% 0.78/1.18 parent0: (222) {G0,W3,D2,L1,V0,M1} { ! equal_lines( skol1, skol2 ) }.
% 0.78/1.18 substitution0:
% 0.78/1.18 end
% 0.78/1.18 permutation0:
% 0.78/1.18 0 ==> 0
% 0.78/1.18 end
% 0.78/1.18
% 0.78/1.18 resolution: (312) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 0.78/1.18 distinct_lines( X, Y ) }.
% 0.78/1.18 parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.78/1.18 parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 0.78/1.18 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 0.78/1.18 substitution0:
% 0.78/1.18 X := X
% 0.78/1.18 end
% 0.78/1.18 substitution1:
% 0.78/1.18 X := X
% 0.78/1.18 Y := Y
% 0.78/1.18 Z := X
% 0.78/1.18 end
% 0.78/1.18
% 0.78/1.18 subsumption: (57) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 0.78/1.18 distinct_lines( X, Y ) }.
% 0.78/1.18 parent0: (312) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 0.78/1.18 distinct_lines( X, Y ) }.
% 0.78/1.18 substitution0:
% 0.78/1.18 X := Y
% 0.78/1.18 Y := X
% 0.78/1.18 end
% 0.78/1.18 permutation0:
% 0.78/1.18 0 ==> 1
% 0.78/1.18 1 ==> 0
% 0.78/1.18 end
% 0.78/1.18
% 0.78/1.18 resolution: (314) {G1,W3,D2,L1,V0,M1} { ! convergent_lines( skol1, skol4 )
% 0.78/1.18 }.
% 0.78/1.18 parent0[1]: (40) {G0,W6,D2,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 0.78/1.18 parallel_lines( X, Y ) }.
% 0.78/1.18 parent1[0]: (49) {G0,W3,D2,L1,V0,M1} I { parallel_lines( skol1, skol4 ) }.
% 0.78/1.18 substitution0:
% 0.78/1.18 X := skol1
% 0.78/1.18 Y := skol4
% 0.78/1.18 end
% 0.78/1.18 substitution1:
% 0.78/1.18 end
% 0.78/1.18
% 0.78/1.18 subsumption: (75) {G1,W3,D2,L1,V0,M1} R(40,49) { ! convergent_lines( skol1
% 0.78/1.18 , skol4 ) }.
% 0.78/1.18 parent0: (314) {G1,W3,D2,L1,V0,M1} { ! convergent_lines( skol1, skol4 )
% 0.78/1.18 }.
% 0.78/1.18 substitution0:
% 0.78/1.18 end
% 0.78/1.18 permutation0:
% 0.78/1.18 0 ==> 0
% 0.78/1.18 end
% 0.78/1.18
% 0.78/1.18 resolution: (315) {G1,W3,D2,L1,V0,M1} { ! convergent_lines( skol2, skol4 )
% 0.78/1.18 }.
% 0.78/1.18 parent0[1]: (40) {G0,W6,D2,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 0.78/1.18 parallel_lines( X, Y ) }.
% 0.78/1.18 parent1[0]: (50) {G0,W3,D2,L1,V0,M1} I { parallel_lines( skol2, skol4 ) }.
% 0.78/1.18 substitution0:
% 0.78/1.18 X := skol2
% 0.78/1.18 Y := skol4
% 0.78/1.18 end
% 0.78/1.18 substitution1:
% 0.78/1.18 end
% 0.78/1.18
% 0.78/1.18 subsumption: (76) {G1,W3,D2,L1,V0,M1} R(40,50) { ! convergent_lines( skol2
% 0.78/1.18 , skol4 ) }.
% 0.78/1.18 parent0: (315) {G1,W3,D2,L1,V0,M1} { ! convergent_lines( skol2, skol4 )
% 0.78/1.18 }.
% 0.78/1.18 substitution0:
% 0.78/1.18 end
% 0.78/1.18 permutation0:
% 0.78/1.18 0 ==> 0
% 0.78/1.18 end
% 0.78/1.18
% 0.78/1.18 resolution: (316) {G1,W3,D2,L1,V0,M1} { distinct_lines( skol1, skol2 ) }.
% 0.78/1.18 parent0[0]: (51) {G0,W3,D2,L1,V0,M1} I { ! equal_lines( skol1, skol2 ) }.
% 0.78/1.18 parent1[1]: (39) {G0,W6,D2,L2,V2,M1} I { distinct_lines( X, Y ),
% 0.78/1.18 equal_lines( X, Y ) }.
% 0.78/1.18 substitution0:
% 0.78/1.18 end
% 0.78/1.18 substitution1:
% 0.78/1.18 X := skol1
% 0.78/1.18 Y := skol2
% 0.78/1.18 end
% 0.78/1.18
% 0.78/1.18 subsumption: (87) {G1,W3,D2,L1,V0,M1} R(39,51) { distinct_lines( skol1,
% 0.78/1.18 skol2 ) }.
% 0.78/1.18 parent0: (316) {G1,W3,D2,L1,V0,M1} { distinct_lines( skol1, skol2 ) }.
% 0.78/1.18 substitution0:
% 0.78/1.18 end
% 0.78/1.18 permutation0:
% 0.78/1.18 0 ==> 0
% 0.78/1.18 end
% 0.78/1.18
% 0.78/1.18 resolution: (317) {G2,W3,D2,L1,V0,M1} { distinct_lines( skol2, skol1 ) }.
% 0.78/1.18 parent0[0]: (57) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 0.78/1.18 distinct_lines( X, Y ) }.
% 0.78/1.18 parent1[0]: (87) {G1,W3,D2,L1,V0,M1} R(39,51) { distinct_lines( skol1,
% 0.78/1.18 skol2 ) }.
% 0.78/1.18 substitution0:
% 0.78/1.18 X := skol2
% 0.78/1.18 Y := skol1
% 0.78/1.18 end
% 0.78/1.18 substitution1:
% 0.78/1.18 end
% 0.78/1.18
% 0.78/1.18 subsumption: (88) {G2,W3,D2,L1,V0,M1} R(87,57) { distinct_lines( skol2,
% 0.78/1.18 skol1 ) }.
% 0.78/1.18 parent0: (317) {G2,W3,D2,L1,V0,M1} { distinct_lines( skol2, skol1 ) }.
% 0.78/1.18 substitution0:
% 0.78/1.18 end
% 0.78/1.18 permutation0:
% 0.78/1.18 0 ==> 0
% 0.78/1.18 end
% 0.78/1.18
% 0.78/1.18 resolution: (318) {G1,W3,D2,L1,V0,M1} { convergent_lines( skol2, skol1 )
% 0.78/1.18 }.
% 0.78/1.18 parent0[1]: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 0.78/1.18 distinct_lines( X, Y ) }.
% 0.78/1.18 parent1[0]: (88) {G2,W3,D2,L1,V0,M1} R(87,57) { distinct_lines( skol2,
% 0.78/1.18 skol1 ) }.
% 0.78/1.18 substitution0:
% 0.78/1.18 X := skol2
% 0.78/1.18 Y := skol1
% 0.78/1.18 end
% 0.78/1.18 substitution1:
% 0.78/1.18 end
% 0.78/1.18
% 0.78/1.18 subsumption: (157) {G3,W3,D2,L1,V0,M1} R(14,88) { convergent_lines( skol2,
% 0.78/1.18 skol1 ) }.
% 0.78/1.18 parent0: (318) {G1,W3,D2,L1,V0,M1} { convergent_lines( skol2, skol1 ) }.
% 0.78/1.18 substitution0:
% 0.78/1.18 end
% 0.78/1.18 permutation0:
% 0.78/1.18 0 ==> 0
% 0.78/1.18 end
% 0.78/1.18
% 0.78/1.18 resolution: (319) {G1,W6,D2,L2,V1,M2} { convergent_lines( skol2, X ),
% 0.78/1.18 convergent_lines( skol1, X ) }.
% 0.78/1.18 parent0[2]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 0.78/1.18 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.78/1.18 parent1[0]: (157) {G3,W3,D2,L1,V0,M1} R(14,88) { convergent_lines( skol2,
% 0.78/1.18 skol1 ) }.
% 0.78/1.18 substitution0:
% 0.78/1.18 X := skol2
% 0.78/1.18 Y := skol1
% 0.78/1.18 Z := X
% 0.78/1.18 end
% 0.78/1.18 substitution1:
% 0.78/1.18 end
% 0.78/1.18
% 0.78/1.18 subsumption: (164) {G4,W6,D2,L2,V1,M1} R(157,5) { convergent_lines( skol1,
% 0.78/1.18 X ), convergent_lines( skol2, X ) }.
% 0.78/1.18 parent0: (319) {G1,W6,D2,L2,V1,M2} { convergent_lines( skol2, X ),
% 0.78/1.18 convergent_lines( skol1, X ) }.
% 0.78/1.18 substitution0:
% 0.78/1.18 X := X
% 0.78/1.18 end
% 0.78/1.18 permutation0:
% 0.78/1.18 0 ==> 1
% 0.78/1.18 1 ==> 0
% 0.78/1.18 end
% 0.78/1.18
% 0.78/1.18 resolution: (320) {G2,W3,D2,L1,V0,M1} { convergent_lines( skol1, skol4 )
% 0.78/1.18 }.
% 0.78/1.18 parent0[0]: (76) {G1,W3,D2,L1,V0,M1} R(40,50) { ! convergent_lines( skol2,
% 0.78/1.18 skol4 ) }.
% 0.78/1.18 parent1[1]: (164) {G4,W6,D2,L2,V1,M1} R(157,5) { convergent_lines( skol1, X
% 0.78/1.18 ), convergent_lines( skol2, X ) }.
% 0.78/1.18 substitution0:
% 0.78/1.18 end
% 0.78/1.18 substitution1:
% 0.78/1.18 X := skol4
% 0.78/1.18 end
% 0.78/1.18
% 0.78/1.18 resolution: (321) {G2,W0,D0,L0,V0,M0} { }.
% 0.78/1.18 parent0[0]: (75) {G1,W3,D2,L1,V0,M1} R(40,49) { ! convergent_lines( skol1,
% 0.78/1.18 skol4 ) }.
% 0.78/1.18 parent1[0]: (320) {G2,W3,D2,L1,V0,M1} { convergent_lines( skol1, skol4 )
% 0.78/1.18 }.
% 0.78/1.18 substitution0:
% 0.78/1.18 end
% 0.78/1.18 substitution1:
% 0.78/1.18 end
% 0.78/1.18
% 0.78/1.18 subsumption: (167) {G5,W0,D0,L0,V0,M0} R(164,76);r(75) { }.
% 0.78/1.18 parent0: (321) {G2,W0,D0,L0,V0,M0} { }.
% 0.78/1.18 substitution0:
% 0.78/1.18 end
% 0.78/1.18 permutation0:
% 0.78/1.18 end
% 0.78/1.18
% 0.78/1.18 Proof check complete!
% 0.78/1.18
% 0.78/1.18 Memory use:
% 0.78/1.18
% 0.78/1.18 space for terms: 3192
% 0.78/1.18 space for clauses: 7733
% 0.78/1.18
% 0.78/1.18
% 0.78/1.18 clauses generated: 409
% 0.78/1.18 clauses kept: 168
% 0.78/1.18 clauses selected: 60
% 0.78/1.18 clauses deleted: 0
% 0.78/1.18 clauses inuse deleted: 0
% 0.78/1.18
% 0.78/1.18 subsentry: 689
% 0.78/1.18 literals s-matched: 509
% 0.78/1.18 literals matched: 479
% 0.78/1.18 full subsumption: 147
% 0.78/1.18
% 0.78/1.18 checksum: -872031960
% 0.78/1.18
% 0.78/1.18
% 0.78/1.18 Bliksem ended
%------------------------------------------------------------------------------