TSTP Solution File: GEO171+3 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO171+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n010.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 02:52:12 EDT 2022
% Result : Theorem 0.72s 1.11s
% Output : Refutation 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GEO171+3 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n010.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 18:22:53 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.72/1.11 *** allocated 10000 integers for termspace/termends
% 0.72/1.11 *** allocated 10000 integers for clauses
% 0.72/1.11 *** allocated 10000 integers for justifications
% 0.72/1.11 Bliksem 1.12
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 Automatic Strategy Selection
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 Clauses:
% 0.72/1.11
% 0.72/1.11 { ! distinct_points( X, X ) }.
% 0.72/1.11 { ! distinct_lines( X, X ) }.
% 0.72/1.11 { ! convergent_lines( X, X ) }.
% 0.72/1.11 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 0.72/1.11 ) }.
% 0.72/1.11 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.72/1.11 }.
% 0.72/1.11 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 0.72/1.11 , Z ) }.
% 0.72/1.11 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 0.72/1.11 , Y ) ) }.
% 0.72/1.11 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 0.72/1.11 , Y ) ) }.
% 0.72/1.11 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.72/1.11 , Y ), X ) }.
% 0.72/1.11 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.72/1.11 , Y ), Y ) }.
% 0.72/1.11 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 0.72/1.11 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 0.72/1.11 apart_point_and_line( Y, T ) }.
% 0.72/1.11 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 0.72/1.11 apart_point_and_line( Z, Y ) }.
% 0.72/1.11 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 0.72/1.11 apart_point_and_line( X, Z ) }.
% 0.72/1.11 { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X,
% 0.72/1.11 Z ) }.
% 0.72/1.11 { ! distinct_lines( X, Y ), convergent_lines( X, Y ) }.
% 0.72/1.11 { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 0.72/1.11 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 0.72/1.11 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 0.72/1.11 apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 0.72/1.11 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.72/1.11 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.72/1.11 , convergent_lines( Y, Z ) }.
% 0.72/1.11 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.72/1.11 , unorthogonal_lines( Y, Z ) }.
% 0.72/1.11 { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 0.72/1.11 { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.72/1.11 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 0.72/1.11 }.
% 0.72/1.11 { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 0.72/1.11 { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 0.72/1.11 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 0.72/1.11 apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ),
% 0.72/1.11 unorthogonal_lines( Y, T ) }.
% 0.72/1.11 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.72/1.11 { alpha2( X, Z ), convergent_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 0.72/1.11 unorthogonal_lines( X, Y ) }.
% 0.72/1.11 { alpha2( X, Z ), unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 0.72/1.11 unorthogonal_lines( X, Y ) }.
% 0.72/1.11 { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 0.72/1.11 { ! alpha2( X, Y ), unorthogonal_lines( Y, X ) }.
% 0.72/1.11 { ! convergent_lines( Y, X ), ! unorthogonal_lines( Y, X ), alpha2( X, Y )
% 0.72/1.11 }.
% 0.72/1.11 { unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ), !
% 0.72/1.11 convergent_lines( X, Y ) }.
% 0.72/1.11 { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line(
% 0.72/1.11 line_connecting( X, Y ) ) }.
% 0.72/1.11 { ! line( X ), ! line( Y ), ! convergent_lines( X, Y ), point(
% 0.72/1.11 intersection_point( X, Y ) ) }.
% 0.72/1.11 { ! line( X ), ! point( Y ), line( parallel_through_point( X, Y ) ) }.
% 0.72/1.11 { ! line( X ), ! point( Y ), line( orthogonal_through_point( X, Y ) ) }.
% 0.72/1.11 { ! equal_points( X, Y ), ! distinct_points( X, Y ) }.
% 0.72/1.11 { distinct_points( X, Y ), equal_points( X, Y ) }.
% 0.72/1.11 { ! equal_lines( X, Y ), ! distinct_lines( X, Y ) }.
% 0.72/1.11 { distinct_lines( X, Y ), equal_lines( X, Y ) }.
% 0.72/1.11 { ! parallel_lines( X, Y ), ! convergent_lines( X, Y ) }.
% 0.72/1.11 { convergent_lines( X, Y ), parallel_lines( X, Y ) }.
% 0.72/1.11 { ! incident_point_and_line( X, Y ), ! apart_point_and_line( X, Y ) }.
% 0.72/1.11 { apart_point_and_line( X, Y ), incident_point_and_line( X, Y ) }.
% 0.72/1.11 { ! orthogonal_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.72/1.11 { unorthogonal_lines( X, Y ), orthogonal_lines( X, Y ) }.
% 0.72/1.11 { convergent_lines( skol1, skol2 ) }.
% 0.72/1.11 { ! distinct_lines( skol1, skol2 ) }.
% 0.72/1.11
% 0.72/1.11 percentage equality = 0.000000, percentage horn = 0.604167
% 0.72/1.11 This a non-horn, non-equality problem
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 Options Used:
% 0.72/1.11
% 0.72/1.11 useres = 1
% 0.72/1.11 useparamod = 0
% 0.72/1.11 useeqrefl = 0
% 0.72/1.11 useeqfact = 0
% 0.72/1.11 usefactor = 1
% 0.72/1.11 usesimpsplitting = 0
% 0.72/1.11 usesimpdemod = 0
% 0.72/1.11 usesimpres = 3
% 0.72/1.11
% 0.72/1.11 resimpinuse = 1000
% 0.72/1.11 resimpclauses = 20000
% 0.72/1.11 substype = standard
% 0.72/1.11 backwardsubs = 1
% 0.72/1.11 selectoldest = 5
% 0.72/1.11
% 0.72/1.11 litorderings [0] = split
% 0.72/1.11 litorderings [1] = liftord
% 0.72/1.11
% 0.72/1.11 termordering = none
% 0.72/1.11
% 0.72/1.11 litapriori = 1
% 0.72/1.11 termapriori = 0
% 0.72/1.11 litaposteriori = 0
% 0.72/1.11 termaposteriori = 0
% 0.72/1.11 demodaposteriori = 0
% 0.72/1.11 ordereqreflfact = 0
% 0.72/1.11
% 0.72/1.11 litselect = none
% 0.72/1.11
% 0.72/1.11 maxweight = 15
% 0.72/1.11 maxdepth = 30000
% 0.72/1.11 maxlength = 115
% 0.72/1.11 maxnrvars = 195
% 0.72/1.11 excuselevel = 1
% 0.72/1.11 increasemaxweight = 1
% 0.72/1.11
% 0.72/1.11 maxselected = 10000000
% 0.72/1.11 maxnrclauses = 10000000
% 0.72/1.11
% 0.72/1.11 showgenerated = 0
% 0.72/1.11 showkept = 0
% 0.72/1.11 showselected = 0
% 0.72/1.11 showdeleted = 0
% 0.72/1.11 showresimp = 1
% 0.72/1.11 showstatus = 2000
% 0.72/1.11
% 0.72/1.11 prologoutput = 0
% 0.72/1.11 nrgoals = 5000000
% 0.72/1.11 totalproof = 1
% 0.72/1.11
% 0.72/1.11 Symbols occurring in the translation:
% 0.72/1.11
% 0.72/1.11 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.72/1.11 . [1, 2] (w:1, o:25, a:1, s:1, b:0),
% 0.72/1.11 ! [4, 1] (w:0, o:18, a:1, s:1, b:0),
% 0.72/1.11 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.72/1.11 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.72/1.11 distinct_points [36, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.72/1.11 distinct_lines [37, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.72/1.11 convergent_lines [38, 2] (w:1, o:49, a:1, s:1, b:0),
% 0.72/1.11 line_connecting [41, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.72/1.11 apart_point_and_line [42, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.72/1.11 intersection_point [43, 2] (w:1, o:54, a:1, s:1, b:0),
% 0.72/1.11 parallel_through_point [46, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.72/1.11 unorthogonal_lines [49, 2] (w:1, o:58, a:1, s:1, b:0),
% 0.72/1.11 orthogonal_through_point [52, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.72/1.11 point [54, 1] (w:1, o:23, a:1, s:1, b:0),
% 0.72/1.11 line [55, 1] (w:1, o:24, a:1, s:1, b:0),
% 0.72/1.11 equal_points [56, 2] (w:1, o:59, a:1, s:1, b:0),
% 0.72/1.11 equal_lines [57, 2] (w:1, o:60, a:1, s:1, b:0),
% 0.72/1.11 parallel_lines [58, 2] (w:1, o:61, a:1, s:1, b:0),
% 0.72/1.11 incident_point_and_line [59, 2] (w:1, o:62, a:1, s:1, b:0),
% 0.72/1.11 orthogonal_lines [60, 2] (w:1, o:56, a:1, s:1, b:0),
% 0.72/1.11 alpha1 [61, 2] (w:1, o:63, a:1, s:1, b:0),
% 0.72/1.11 alpha2 [62, 2] (w:1, o:64, a:1, s:1, b:0),
% 0.72/1.11 skol1 [63, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.72/1.11 skol2 [64, 0] (w:1, o:17, a:1, s:1, b:0).
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 Starting Search:
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 Bliksems!, er is een bewijs:
% 0.72/1.11 % SZS status Theorem
% 0.72/1.11 % SZS output start Refutation
% 0.72/1.11
% 0.72/1.11 (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.72/1.11 (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.72/1.11 (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.72/1.11 , ! distinct_lines( X, Y ) }.
% 0.72/1.11 (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), convergent_lines( Y,
% 0.72/1.11 Z ), ! convergent_lines( X, Y ) }.
% 0.72/1.11 (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ), convergent_lines(
% 0.72/1.11 X, Z ), distinct_lines( Y, Z ) }.
% 0.72/1.11 (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines( parallel_through_point( Y
% 0.72/1.11 , X ), Y ) }.
% 0.72/1.11 (46) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 ) }.
% 0.72/1.11 (47) {G0,W3,D2,L1,V0,M1} I { ! distinct_lines( skol1, skol2 ) }.
% 0.72/1.11 (55) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 0.72/1.11 ( X, Y ) }.
% 0.72/1.11 (58) {G2,W3,D2,L1,V0,M1} R(55,47) { ! distinct_lines( skol2, skol1 ) }.
% 0.72/1.11 (68) {G1,W6,D2,L2,V1,M1} R(5,46) { convergent_lines( skol1, X ),
% 0.72/1.11 convergent_lines( skol2, X ) }.
% 0.72/1.11 (69) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.72/1.11 convergent_lines( X, Y ) }.
% 0.72/1.11 (112) {G2,W6,D2,L2,V1,M2} R(68,69) { convergent_lines( X, skol2 ),
% 0.72/1.11 convergent_lines( skol1, X ) }.
% 0.72/1.11 (128) {G3,W6,D2,L2,V1,M1} R(112,69) { convergent_lines( X, skol1 ),
% 0.72/1.11 convergent_lines( X, skol2 ) }.
% 0.72/1.11 (154) {G4,W3,D2,L1,V1,M1} R(13,58);r(128) { convergent_lines( X, skol1 )
% 0.72/1.11 }.
% 0.72/1.11 (159) {G5,W0,D0,L0,V0,M0} R(154,15) { }.
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 % SZS output end Refutation
% 0.72/1.11 found a proof!
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 Unprocessed initial clauses:
% 0.72/1.11
% 0.72/1.11 (161) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 0.72/1.11 (162) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.72/1.11 (163) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 0.72/1.11 (164) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 0.72/1.11 , Z ), distinct_points( Y, Z ) }.
% 0.72/1.11 (165) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X, Z
% 0.72/1.11 ), distinct_lines( Y, Z ) }.
% 0.72/1.11 (166) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines(
% 0.72/1.11 X, Z ), convergent_lines( Y, Z ) }.
% 0.72/1.11 (167) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.72/1.11 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 0.72/1.11 (168) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.72/1.11 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 0.72/1.11 (169) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 0.72/1.11 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 0.72/1.11 (170) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 0.72/1.11 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 0.72/1.11 (171) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines(
% 0.72/1.11 Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 0.72/1.11 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 0.72/1.11 (172) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 0.72/1.11 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 0.72/1.11 (173) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ), distinct_lines
% 0.72/1.11 ( Y, Z ), apart_point_and_line( X, Z ) }.
% 0.72/1.11 (174) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), distinct_lines( Y
% 0.72/1.11 , Z ), convergent_lines( X, Z ) }.
% 0.72/1.11 (175) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ), convergent_lines( X
% 0.72/1.11 , Y ) }.
% 0.72/1.11 (176) {G0,W5,D3,L1,V2,M1} { ! convergent_lines( parallel_through_point( Y
% 0.72/1.11 , X ), Y ) }.
% 0.72/1.11 (177) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.72/1.11 parallel_through_point( Y, X ) ) }.
% 0.72/1.11 (178) {G0,W12,D2,L4,V3,M4} { ! distinct_lines( X, Y ),
% 0.72/1.11 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 0.72/1.11 convergent_lines( X, Y ) }.
% 0.72/1.11 (179) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines(
% 0.72/1.11 X, Y ) }.
% 0.72/1.11 (180) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.72/1.11 unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 0.72/1.11 (181) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.72/1.11 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 0.72/1.11 }.
% 0.72/1.11 (182) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 0.72/1.11 (183) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 0.72/1.11 }.
% 0.72/1.11 (184) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( X, Y ), !
% 0.72/1.11 unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 0.72/1.11 (185) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines( orthogonal_through_point
% 0.72/1.11 ( Y, X ), Y ) }.
% 0.72/1.11 (186) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.72/1.11 orthogonal_through_point( Y, X ) ) }.
% 0.72/1.11 (187) {G0,W15,D2,L5,V4,M5} { ! distinct_lines( X, Y ),
% 0.72/1.11 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 0.72/1.11 unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 0.72/1.11 (188) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines(
% 0.72/1.11 X, Y ) }.
% 0.72/1.11 (189) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), convergent_lines( Z, Y ), !
% 0.72/1.11 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.72/1.11 (190) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), unorthogonal_lines( Z, Y ), !
% 0.72/1.11 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.72/1.11 (191) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 0.72/1.11 (192) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), unorthogonal_lines( Y, X )
% 0.72/1.11 }.
% 0.72/1.11 (193) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( Y, X ), !
% 0.72/1.11 unorthogonal_lines( Y, X ), alpha2( X, Y ) }.
% 0.72/1.11 (194) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ), unorthogonal_lines
% 0.72/1.11 ( Z, Y ), ! convergent_lines( X, Y ) }.
% 0.72/1.11 (195) {G0,W11,D3,L4,V2,M4} { ! point( X ), ! point( Y ), ! distinct_points
% 0.72/1.11 ( X, Y ), line( line_connecting( X, Y ) ) }.
% 0.72/1.11 (196) {G0,W11,D3,L4,V2,M4} { ! line( X ), ! line( Y ), ! convergent_lines
% 0.72/1.11 ( X, Y ), point( intersection_point( X, Y ) ) }.
% 0.72/1.11 (197) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 0.72/1.11 parallel_through_point( X, Y ) ) }.
% 0.72/1.11 (198) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 0.72/1.11 orthogonal_through_point( X, Y ) ) }.
% 0.72/1.11 (199) {G0,W6,D2,L2,V2,M2} { ! equal_points( X, Y ), ! distinct_points( X,
% 0.72/1.11 Y ) }.
% 0.72/1.11 (200) {G0,W6,D2,L2,V2,M2} { distinct_points( X, Y ), equal_points( X, Y )
% 0.72/1.11 }.
% 0.72/1.11 (201) {G0,W6,D2,L2,V2,M2} { ! equal_lines( X, Y ), ! distinct_lines( X, Y
% 0.72/1.11 ) }.
% 0.72/1.11 (202) {G0,W6,D2,L2,V2,M2} { distinct_lines( X, Y ), equal_lines( X, Y )
% 0.72/1.11 }.
% 0.72/1.11 (203) {G0,W6,D2,L2,V2,M2} { ! parallel_lines( X, Y ), ! convergent_lines(
% 0.72/1.11 X, Y ) }.
% 0.72/1.11 (204) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), parallel_lines( X, Y
% 0.72/1.11 ) }.
% 0.72/1.11 (205) {G0,W6,D2,L2,V2,M2} { ! incident_point_and_line( X, Y ), !
% 0.72/1.11 apart_point_and_line( X, Y ) }.
% 0.72/1.11 (206) {G0,W6,D2,L2,V2,M2} { apart_point_and_line( X, Y ),
% 0.72/1.11 incident_point_and_line( X, Y ) }.
% 0.72/1.11 (207) {G0,W6,D2,L2,V2,M2} { ! orthogonal_lines( X, Y ), !
% 0.72/1.11 unorthogonal_lines( X, Y ) }.
% 0.72/1.11 (208) {G0,W6,D2,L2,V2,M2} { unorthogonal_lines( X, Y ), orthogonal_lines(
% 0.72/1.11 X, Y ) }.
% 0.72/1.11 (209) {G0,W3,D2,L1,V0,M1} { convergent_lines( skol1, skol2 ) }.
% 0.72/1.11 (210) {G0,W3,D2,L1,V0,M1} { ! distinct_lines( skol1, skol2 ) }.
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 Total Proof:
% 0.72/1.11
% 0.72/1.11 subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.72/1.11 parent0: (162) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 0 ==> 0
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 subsumption: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.72/1.11 parent0: (163) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 0 ==> 0
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 0.72/1.11 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 0.72/1.11 parent0: (165) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ),
% 0.72/1.11 distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 Y := Y
% 0.72/1.11 Z := Z
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 0 ==> 2
% 0.72/1.11 1 ==> 0
% 0.72/1.11 2 ==> 1
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 subsumption: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 0.72/1.11 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.72/1.11 parent0: (166) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 0.72/1.11 convergent_lines( X, Z ), convergent_lines( Y, Z ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 Y := Y
% 0.72/1.11 Z := Z
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 0 ==> 2
% 0.72/1.11 1 ==> 0
% 0.72/1.11 2 ==> 1
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 subsumption: (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ),
% 0.72/1.11 convergent_lines( X, Z ), distinct_lines( Y, Z ) }.
% 0.72/1.11 parent0: (174) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 0.72/1.11 distinct_lines( Y, Z ), convergent_lines( X, Z ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 Y := Y
% 0.72/1.11 Z := Z
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 0 ==> 0
% 0.72/1.11 1 ==> 2
% 0.72/1.11 2 ==> 1
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 subsumption: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 0.72/1.11 parallel_through_point( Y, X ), Y ) }.
% 0.72/1.11 parent0: (176) {G0,W5,D3,L1,V2,M1} { ! convergent_lines(
% 0.72/1.11 parallel_through_point( Y, X ), Y ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 Y := Y
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 0 ==> 0
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 subsumption: (46) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 )
% 0.72/1.11 }.
% 0.72/1.11 parent0: (209) {G0,W3,D2,L1,V0,M1} { convergent_lines( skol1, skol2 ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 0 ==> 0
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 subsumption: (47) {G0,W3,D2,L1,V0,M1} I { ! distinct_lines( skol1, skol2 )
% 0.72/1.11 }.
% 0.72/1.11 parent0: (210) {G0,W3,D2,L1,V0,M1} { ! distinct_lines( skol1, skol2 ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 0 ==> 0
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 resolution: (264) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 0.72/1.11 distinct_lines( X, Y ) }.
% 0.72/1.11 parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.72/1.11 parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 0.72/1.11 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 end
% 0.72/1.11 substitution1:
% 0.72/1.11 X := X
% 0.72/1.11 Y := Y
% 0.72/1.11 Z := X
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 subsumption: (55) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 0.72/1.11 distinct_lines( X, Y ) }.
% 0.72/1.11 parent0: (264) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 0.72/1.11 distinct_lines( X, Y ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := Y
% 0.72/1.11 Y := X
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 0 ==> 1
% 0.72/1.11 1 ==> 0
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 resolution: (266) {G1,W3,D2,L1,V0,M1} { ! distinct_lines( skol2, skol1 )
% 0.72/1.11 }.
% 0.72/1.11 parent0[0]: (47) {G0,W3,D2,L1,V0,M1} I { ! distinct_lines( skol1, skol2 )
% 0.72/1.11 }.
% 0.72/1.11 parent1[1]: (55) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 0.72/1.11 distinct_lines( X, Y ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 end
% 0.72/1.11 substitution1:
% 0.72/1.11 X := skol1
% 0.72/1.11 Y := skol2
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 subsumption: (58) {G2,W3,D2,L1,V0,M1} R(55,47) { ! distinct_lines( skol2,
% 0.72/1.11 skol1 ) }.
% 0.72/1.11 parent0: (266) {G1,W3,D2,L1,V0,M1} { ! distinct_lines( skol2, skol1 ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 0 ==> 0
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 resolution: (267) {G1,W6,D2,L2,V1,M2} { convergent_lines( skol1, X ),
% 0.72/1.11 convergent_lines( skol2, X ) }.
% 0.72/1.11 parent0[2]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 0.72/1.11 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.72/1.11 parent1[0]: (46) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 )
% 0.72/1.11 }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := skol1
% 0.72/1.11 Y := skol2
% 0.72/1.11 Z := X
% 0.72/1.11 end
% 0.72/1.11 substitution1:
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 subsumption: (68) {G1,W6,D2,L2,V1,M1} R(5,46) { convergent_lines( skol1, X
% 0.72/1.11 ), convergent_lines( skol2, X ) }.
% 0.72/1.11 parent0: (267) {G1,W6,D2,L2,V1,M2} { convergent_lines( skol1, X ),
% 0.72/1.11 convergent_lines( skol2, X ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 0 ==> 0
% 0.72/1.11 1 ==> 1
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 resolution: (268) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 0.72/1.11 convergent_lines( X, Y ) }.
% 0.72/1.11 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.72/1.11 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 0.72/1.11 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 end
% 0.72/1.11 substitution1:
% 0.72/1.11 X := X
% 0.72/1.11 Y := Y
% 0.72/1.11 Z := X
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 subsumption: (69) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.72/1.11 convergent_lines( X, Y ) }.
% 0.72/1.11 parent0: (268) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 0.72/1.11 convergent_lines( X, Y ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := Y
% 0.72/1.11 Y := X
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 0 ==> 1
% 0.72/1.11 1 ==> 0
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 resolution: (271) {G2,W6,D2,L2,V1,M2} { convergent_lines( X, skol2 ),
% 0.72/1.11 convergent_lines( skol1, X ) }.
% 0.72/1.11 parent0[0]: (69) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.72/1.11 convergent_lines( X, Y ) }.
% 0.72/1.11 parent1[1]: (68) {G1,W6,D2,L2,V1,M1} R(5,46) { convergent_lines( skol1, X )
% 0.72/1.11 , convergent_lines( skol2, X ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 Y := skol2
% 0.72/1.11 end
% 0.72/1.11 substitution1:
% 0.72/1.11 X := X
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 subsumption: (112) {G2,W6,D2,L2,V1,M2} R(68,69) { convergent_lines( X,
% 0.72/1.11 skol2 ), convergent_lines( skol1, X ) }.
% 0.72/1.11 parent0: (271) {G2,W6,D2,L2,V1,M2} { convergent_lines( X, skol2 ),
% 0.72/1.11 convergent_lines( skol1, X ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 0 ==> 0
% 0.72/1.11 1 ==> 1
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 resolution: (273) {G2,W6,D2,L2,V1,M2} { convergent_lines( X, skol1 ),
% 0.72/1.11 convergent_lines( X, skol2 ) }.
% 0.72/1.11 parent0[0]: (69) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.72/1.11 convergent_lines( X, Y ) }.
% 0.72/1.11 parent1[1]: (112) {G2,W6,D2,L2,V1,M2} R(68,69) { convergent_lines( X, skol2
% 0.72/1.11 ), convergent_lines( skol1, X ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 Y := skol1
% 0.72/1.11 end
% 0.72/1.11 substitution1:
% 0.72/1.11 X := X
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 subsumption: (128) {G3,W6,D2,L2,V1,M1} R(112,69) { convergent_lines( X,
% 0.72/1.11 skol1 ), convergent_lines( X, skol2 ) }.
% 0.72/1.11 parent0: (273) {G2,W6,D2,L2,V1,M2} { convergent_lines( X, skol1 ),
% 0.72/1.11 convergent_lines( X, skol2 ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 0 ==> 0
% 0.72/1.11 1 ==> 1
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 resolution: (274) {G1,W6,D2,L2,V1,M2} { ! convergent_lines( X, skol2 ),
% 0.72/1.11 convergent_lines( X, skol1 ) }.
% 0.72/1.11 parent0[0]: (58) {G2,W3,D2,L1,V0,M1} R(55,47) { ! distinct_lines( skol2,
% 0.72/1.11 skol1 ) }.
% 0.72/1.11 parent1[2]: (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ),
% 0.72/1.11 convergent_lines( X, Z ), distinct_lines( Y, Z ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 end
% 0.72/1.11 substitution1:
% 0.72/1.11 X := X
% 0.72/1.11 Y := skol2
% 0.72/1.11 Z := skol1
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 resolution: (275) {G2,W6,D2,L2,V1,M2} { convergent_lines( X, skol1 ),
% 0.72/1.11 convergent_lines( X, skol1 ) }.
% 0.72/1.11 parent0[0]: (274) {G1,W6,D2,L2,V1,M2} { ! convergent_lines( X, skol2 ),
% 0.72/1.11 convergent_lines( X, skol1 ) }.
% 0.72/1.11 parent1[1]: (128) {G3,W6,D2,L2,V1,M1} R(112,69) { convergent_lines( X,
% 0.72/1.11 skol1 ), convergent_lines( X, skol2 ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 end
% 0.72/1.11 substitution1:
% 0.72/1.11 X := X
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 factor: (276) {G2,W3,D2,L1,V1,M1} { convergent_lines( X, skol1 ) }.
% 0.72/1.11 parent0[0, 1]: (275) {G2,W6,D2,L2,V1,M2} { convergent_lines( X, skol1 ),
% 0.72/1.11 convergent_lines( X, skol1 ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 subsumption: (154) {G4,W3,D2,L1,V1,M1} R(13,58);r(128) { convergent_lines(
% 0.72/1.11 X, skol1 ) }.
% 0.72/1.11 parent0: (276) {G2,W3,D2,L1,V1,M1} { convergent_lines( X, skol1 ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 0 ==> 0
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 resolution: (277) {G1,W0,D0,L0,V0,M0} { }.
% 0.72/1.11 parent0[0]: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 0.72/1.11 parallel_through_point( Y, X ), Y ) }.
% 0.72/1.11 parent1[0]: (154) {G4,W3,D2,L1,V1,M1} R(13,58);r(128) { convergent_lines( X
% 0.72/1.11 , skol1 ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 Y := skol1
% 0.72/1.11 end
% 0.72/1.11 substitution1:
% 0.72/1.11 X := parallel_through_point( skol1, X )
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 subsumption: (159) {G5,W0,D0,L0,V0,M0} R(154,15) { }.
% 0.72/1.11 parent0: (277) {G1,W0,D0,L0,V0,M0} { }.
% 0.72/1.11 substitution0:
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 Proof check complete!
% 0.72/1.11
% 0.72/1.11 Memory use:
% 0.72/1.11
% 0.72/1.11 space for terms: 3061
% 0.72/1.11 space for clauses: 7350
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 clauses generated: 409
% 0.72/1.11 clauses kept: 160
% 0.72/1.11 clauses selected: 57
% 0.72/1.11 clauses deleted: 0
% 0.72/1.11 clauses inuse deleted: 0
% 0.72/1.11
% 0.72/1.11 subsentry: 695
% 0.72/1.11 literals s-matched: 521
% 0.72/1.11 literals matched: 501
% 0.72/1.11 full subsumption: 161
% 0.72/1.11
% 0.72/1.11 checksum: 1713756402
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 Bliksem ended
%------------------------------------------------------------------------------