TSTP Solution File: GEO178+3 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO178+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n023.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 02:52:19 EDT 2022
% Result : Theorem 0.70s 1.08s
% Output : Refutation 0.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GEO178+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : bliksem %s
% 0.12/0.32 % Computer : n023.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.33 % DateTime : Fri Jun 17 19:09:49 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.70/1.08 *** allocated 10000 integers for termspace/termends
% 0.70/1.08 *** allocated 10000 integers for clauses
% 0.70/1.08 *** allocated 10000 integers for justifications
% 0.70/1.08 Bliksem 1.12
% 0.70/1.08
% 0.70/1.08
% 0.70/1.08 Automatic Strategy Selection
% 0.70/1.08
% 0.70/1.08
% 0.70/1.08 Clauses:
% 0.70/1.08
% 0.70/1.08 { ! distinct_points( X, X ) }.
% 0.70/1.08 { ! distinct_lines( X, X ) }.
% 0.70/1.08 { ! convergent_lines( X, X ) }.
% 0.70/1.08 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 0.70/1.08 ) }.
% 0.70/1.08 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.70/1.08 }.
% 0.70/1.08 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 0.70/1.08 , Z ) }.
% 0.70/1.08 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 0.70/1.08 , Y ) ) }.
% 0.70/1.08 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 0.70/1.08 , Y ) ) }.
% 0.70/1.08 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.70/1.08 , Y ), X ) }.
% 0.70/1.08 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.70/1.08 , Y ), Y ) }.
% 0.70/1.08 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 0.70/1.08 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 0.70/1.08 apart_point_and_line( Y, T ) }.
% 0.70/1.08 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 0.70/1.08 apart_point_and_line( Z, Y ) }.
% 0.70/1.08 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 0.70/1.08 apart_point_and_line( X, Z ) }.
% 0.70/1.08 { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X,
% 0.70/1.08 Z ) }.
% 0.70/1.08 { ! distinct_lines( X, Y ), convergent_lines( X, Y ) }.
% 0.70/1.08 { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 0.70/1.08 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 0.70/1.08 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 0.70/1.08 apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 0.70/1.08 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.70/1.08 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.70/1.08 , convergent_lines( Y, Z ) }.
% 0.70/1.08 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.70/1.08 , unorthogonal_lines( Y, Z ) }.
% 0.70/1.08 { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 0.70/1.08 { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.70/1.08 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 0.70/1.08 }.
% 0.70/1.08 { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 0.70/1.08 { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 0.70/1.08 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 0.70/1.08 apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ),
% 0.70/1.08 unorthogonal_lines( Y, T ) }.
% 0.70/1.08 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.70/1.08 { alpha2( X, Z ), convergent_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 0.70/1.08 unorthogonal_lines( X, Y ) }.
% 0.70/1.08 { alpha2( X, Z ), unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 0.70/1.08 unorthogonal_lines( X, Y ) }.
% 0.70/1.08 { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 0.70/1.08 { ! alpha2( X, Y ), unorthogonal_lines( Y, X ) }.
% 0.70/1.08 { ! convergent_lines( Y, X ), ! unorthogonal_lines( Y, X ), alpha2( X, Y )
% 0.70/1.08 }.
% 0.70/1.08 { unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ), !
% 0.70/1.08 convergent_lines( X, Y ) }.
% 0.70/1.08 { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line(
% 0.70/1.08 line_connecting( X, Y ) ) }.
% 0.70/1.08 { ! line( X ), ! line( Y ), ! convergent_lines( X, Y ), point(
% 0.70/1.08 intersection_point( X, Y ) ) }.
% 0.70/1.08 { ! line( X ), ! point( Y ), line( parallel_through_point( X, Y ) ) }.
% 0.70/1.08 { ! line( X ), ! point( Y ), line( orthogonal_through_point( X, Y ) ) }.
% 0.70/1.08 { ! equal_points( X, Y ), ! distinct_points( X, Y ) }.
% 0.70/1.08 { distinct_points( X, Y ), equal_points( X, Y ) }.
% 0.70/1.08 { ! equal_lines( X, Y ), ! distinct_lines( X, Y ) }.
% 0.70/1.08 { distinct_lines( X, Y ), equal_lines( X, Y ) }.
% 0.70/1.08 { ! parallel_lines( X, Y ), ! convergent_lines( X, Y ) }.
% 0.70/1.08 { convergent_lines( X, Y ), parallel_lines( X, Y ) }.
% 0.70/1.08 { ! incident_point_and_line( X, Y ), ! apart_point_and_line( X, Y ) }.
% 0.70/1.08 { apart_point_and_line( X, Y ), incident_point_and_line( X, Y ) }.
% 0.70/1.08 { ! orthogonal_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.70/1.08 { unorthogonal_lines( X, Y ), orthogonal_lines( X, Y ) }.
% 0.70/1.08 { distinct_points( skol1, skol2 ) }.
% 0.70/1.08 { apart_point_and_line( skol3, line_connecting( skol1, skol2 ) ) }.
% 0.70/1.08 { ! distinct_points( skol3, skol1 ), ! distinct_points( skol3, skol2 ) }.
% 0.70/1.08
% 0.70/1.08 percentage equality = 0.000000, percentage horn = 0.612245
% 0.70/1.08 This a non-horn, non-equality problem
% 0.70/1.08
% 0.70/1.08
% 0.70/1.08 Options Used:
% 0.70/1.08
% 0.70/1.08 useres = 1
% 0.70/1.08 useparamod = 0
% 0.70/1.08 useeqrefl = 0
% 0.70/1.08 useeqfact = 0
% 0.70/1.08 usefactor = 1
% 0.70/1.08 usesimpsplitting = 0
% 0.70/1.08 usesimpdemod = 0
% 0.70/1.08 usesimpres = 3
% 0.70/1.08
% 0.70/1.08 resimpinuse = 1000
% 0.70/1.08 resimpclauses = 20000
% 0.70/1.08 substype = standard
% 0.70/1.08 backwardsubs = 1
% 0.70/1.08 selectoldest = 5
% 0.70/1.08
% 0.70/1.08 litorderings [0] = split
% 0.70/1.08 litorderings [1] = liftord
% 0.70/1.08
% 0.70/1.08 termordering = none
% 0.70/1.08
% 0.70/1.08 litapriori = 1
% 0.70/1.08 termapriori = 0
% 0.70/1.08 litaposteriori = 0
% 0.70/1.08 termaposteriori = 0
% 0.70/1.08 demodaposteriori = 0
% 0.70/1.08 ordereqreflfact = 0
% 0.70/1.08
% 0.70/1.08 litselect = none
% 0.70/1.08
% 0.70/1.08 maxweight = 15
% 0.70/1.08 maxdepth = 30000
% 0.70/1.08 maxlength = 115
% 0.70/1.08 maxnrvars = 195
% 0.70/1.08 excuselevel = 1
% 0.70/1.08 increasemaxweight = 1
% 0.70/1.08
% 0.70/1.08 maxselected = 10000000
% 0.70/1.08 maxnrclauses = 10000000
% 0.70/1.08
% 0.70/1.08 showgenerated = 0
% 0.70/1.08 showkept = 0
% 0.70/1.08 showselected = 0
% 0.70/1.08 showdeleted = 0
% 0.70/1.08 showresimp = 1
% 0.70/1.08 showstatus = 2000
% 0.70/1.08
% 0.70/1.08 prologoutput = 0
% 0.70/1.08 nrgoals = 5000000
% 0.70/1.08 totalproof = 1
% 0.70/1.08
% 0.70/1.08 Symbols occurring in the translation:
% 0.70/1.08
% 0.70/1.08 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.70/1.08 . [1, 2] (w:1, o:26, a:1, s:1, b:0),
% 0.70/1.08 ! [4, 1] (w:0, o:19, a:1, s:1, b:0),
% 0.70/1.08 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.70/1.08 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.70/1.08 distinct_points [36, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.70/1.08 distinct_lines [37, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.70/1.08 convergent_lines [38, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.70/1.08 line_connecting [41, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.70/1.08 apart_point_and_line [42, 2] (w:1, o:54, a:1, s:1, b:0),
% 0.70/1.08 intersection_point [43, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.70/1.08 parallel_through_point [46, 2] (w:1, o:58, a:1, s:1, b:0),
% 0.70/1.08 unorthogonal_lines [49, 2] (w:1, o:59, a:1, s:1, b:0),
% 0.70/1.08 orthogonal_through_point [52, 2] (w:1, o:56, a:1, s:1, b:0),
% 0.70/1.08 point [54, 1] (w:1, o:24, a:1, s:1, b:0),
% 0.70/1.08 line [55, 1] (w:1, o:25, a:1, s:1, b:0),
% 0.70/1.08 equal_points [56, 2] (w:1, o:60, a:1, s:1, b:0),
% 0.70/1.08 equal_lines [57, 2] (w:1, o:61, a:1, s:1, b:0),
% 0.70/1.08 parallel_lines [58, 2] (w:1, o:62, a:1, s:1, b:0),
% 0.70/1.08 incident_point_and_line [59, 2] (w:1, o:63, a:1, s:1, b:0),
% 0.70/1.08 orthogonal_lines [60, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.70/1.08 alpha1 [61, 2] (w:1, o:64, a:1, s:1, b:0),
% 0.70/1.08 alpha2 [62, 2] (w:1, o:65, a:1, s:1, b:0),
% 0.70/1.08 skol1 [63, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.70/1.08 skol2 [64, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.70/1.08 skol3 [65, 0] (w:1, o:18, a:1, s:1, b:0).
% 0.70/1.08
% 0.70/1.08
% 0.70/1.08 Starting Search:
% 0.70/1.08
% 0.70/1.08
% 0.70/1.08 Bliksems!, er is een bewijs:
% 0.70/1.08 % SZS status Theorem
% 0.70/1.08 % SZS output start Refutation
% 0.70/1.08
% 0.70/1.08 (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.70/1.08 (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.70/1.08 , ! distinct_lines( X, Y ) }.
% 0.70/1.08 (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), apart_point_and_line(
% 0.70/1.08 X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.70/1.08 (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! distinct_lines( X
% 0.70/1.08 , Y ) }.
% 0.70/1.08 (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines( parallel_through_point( Y
% 0.70/1.08 , X ), Y ) }.
% 0.70/1.08 (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.70/1.08 parallel_through_point( Y, X ) ) }.
% 0.70/1.08 (47) {G0,W5,D3,L1,V0,M1} I { apart_point_and_line( skol3, line_connecting(
% 0.70/1.08 skol1, skol2 ) ) }.
% 0.70/1.08 (55) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 0.70/1.08 ( X, Y ) }.
% 0.70/1.08 (102) {G2,W6,D2,L2,V2,M1} R(14,55) { convergent_lines( X, Y ), !
% 0.70/1.08 distinct_lines( Y, X ) }.
% 0.70/1.08 (142) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X,
% 0.70/1.08 parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.70/1.08 (146) {G2,W7,D3,L1,V1,M1} R(142,47) { distinct_lines( line_connecting(
% 0.70/1.08 skol1, skol2 ), parallel_through_point( X, skol3 ) ) }.
% 0.70/1.08 (147) {G3,W7,D3,L1,V1,M1} R(146,102) { convergent_lines(
% 0.70/1.08 parallel_through_point( X, skol3 ), line_connecting( skol1, skol2 ) ) }.
% 0.70/1.08 (152) {G4,W0,D0,L0,V0,M0} R(147,15) { }.
% 0.70/1.08
% 0.70/1.08
% 0.70/1.08 % SZS output end Refutation
% 0.70/1.08 found a proof!
% 0.70/1.08
% 0.70/1.08
% 0.70/1.08 Unprocessed initial clauses:
% 0.70/1.08
% 0.70/1.08 (154) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 0.70/1.08 (155) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.70/1.08 (156) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 0.70/1.08 (157) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 0.70/1.08 , Z ), distinct_points( Y, Z ) }.
% 0.70/1.08 (158) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X, Z
% 0.70/1.08 ), distinct_lines( Y, Z ) }.
% 0.70/1.08 (159) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines(
% 0.70/1.08 X, Z ), convergent_lines( Y, Z ) }.
% 0.70/1.08 (160) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.70/1.08 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 0.70/1.08 (161) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.70/1.08 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 0.70/1.08 (162) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 0.70/1.08 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 0.70/1.08 (163) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 0.70/1.08 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 0.70/1.08 (164) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines(
% 0.70/1.08 Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 0.70/1.08 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 0.70/1.08 (165) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 0.70/1.08 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 0.70/1.08 (166) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ), distinct_lines
% 0.70/1.08 ( Y, Z ), apart_point_and_line( X, Z ) }.
% 0.70/1.08 (167) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), distinct_lines( Y
% 0.70/1.08 , Z ), convergent_lines( X, Z ) }.
% 0.70/1.08 (168) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ), convergent_lines( X
% 0.70/1.08 , Y ) }.
% 0.70/1.08 (169) {G0,W5,D3,L1,V2,M1} { ! convergent_lines( parallel_through_point( Y
% 0.70/1.08 , X ), Y ) }.
% 0.70/1.08 (170) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.70/1.08 parallel_through_point( Y, X ) ) }.
% 0.70/1.08 (171) {G0,W12,D2,L4,V3,M4} { ! distinct_lines( X, Y ),
% 0.70/1.08 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 0.70/1.08 convergent_lines( X, Y ) }.
% 0.70/1.08 (172) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines(
% 0.70/1.08 X, Y ) }.
% 0.70/1.08 (173) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.70/1.08 unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 0.70/1.08 (174) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.70/1.08 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 0.70/1.08 }.
% 0.70/1.08 (175) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 0.70/1.08 (176) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 0.70/1.08 }.
% 0.70/1.08 (177) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( X, Y ), !
% 0.70/1.08 unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 0.70/1.08 (178) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines( orthogonal_through_point
% 0.70/1.08 ( Y, X ), Y ) }.
% 0.70/1.08 (179) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.70/1.08 orthogonal_through_point( Y, X ) ) }.
% 0.70/1.08 (180) {G0,W15,D2,L5,V4,M5} { ! distinct_lines( X, Y ),
% 0.70/1.08 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 0.70/1.08 unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 0.70/1.08 (181) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines(
% 0.70/1.08 X, Y ) }.
% 0.70/1.08 (182) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), convergent_lines( Z, Y ), !
% 0.70/1.08 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.70/1.08 (183) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), unorthogonal_lines( Z, Y ), !
% 0.70/1.08 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.70/1.08 (184) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 0.70/1.08 (185) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), unorthogonal_lines( Y, X )
% 0.70/1.08 }.
% 0.70/1.08 (186) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( Y, X ), !
% 0.70/1.08 unorthogonal_lines( Y, X ), alpha2( X, Y ) }.
% 0.70/1.08 (187) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ), unorthogonal_lines
% 0.70/1.08 ( Z, Y ), ! convergent_lines( X, Y ) }.
% 0.70/1.08 (188) {G0,W11,D3,L4,V2,M4} { ! point( X ), ! point( Y ), ! distinct_points
% 0.70/1.08 ( X, Y ), line( line_connecting( X, Y ) ) }.
% 0.70/1.08 (189) {G0,W11,D3,L4,V2,M4} { ! line( X ), ! line( Y ), ! convergent_lines
% 0.70/1.08 ( X, Y ), point( intersection_point( X, Y ) ) }.
% 0.70/1.08 (190) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 0.70/1.08 parallel_through_point( X, Y ) ) }.
% 0.70/1.08 (191) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 0.70/1.08 orthogonal_through_point( X, Y ) ) }.
% 0.70/1.08 (192) {G0,W6,D2,L2,V2,M2} { ! equal_points( X, Y ), ! distinct_points( X,
% 0.70/1.08 Y ) }.
% 0.70/1.08 (193) {G0,W6,D2,L2,V2,M2} { distinct_points( X, Y ), equal_points( X, Y )
% 0.70/1.08 }.
% 0.70/1.08 (194) {G0,W6,D2,L2,V2,M2} { ! equal_lines( X, Y ), ! distinct_lines( X, Y
% 0.70/1.08 ) }.
% 0.70/1.08 (195) {G0,W6,D2,L2,V2,M2} { distinct_lines( X, Y ), equal_lines( X, Y )
% 0.70/1.08 }.
% 0.70/1.08 (196) {G0,W6,D2,L2,V2,M2} { ! parallel_lines( X, Y ), ! convergent_lines(
% 0.70/1.08 X, Y ) }.
% 0.70/1.08 (197) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), parallel_lines( X, Y
% 0.70/1.08 ) }.
% 0.70/1.08 (198) {G0,W6,D2,L2,V2,M2} { ! incident_point_and_line( X, Y ), !
% 0.70/1.08 apart_point_and_line( X, Y ) }.
% 0.70/1.08 (199) {G0,W6,D2,L2,V2,M2} { apart_point_and_line( X, Y ),
% 0.70/1.08 incident_point_and_line( X, Y ) }.
% 0.70/1.08 (200) {G0,W6,D2,L2,V2,M2} { ! orthogonal_lines( X, Y ), !
% 0.70/1.08 unorthogonal_lines( X, Y ) }.
% 0.70/1.08 (201) {G0,W6,D2,L2,V2,M2} { unorthogonal_lines( X, Y ), orthogonal_lines(
% 0.70/1.08 X, Y ) }.
% 0.70/1.08 (202) {G0,W3,D2,L1,V0,M1} { distinct_points( skol1, skol2 ) }.
% 0.70/1.08 (203) {G0,W5,D3,L1,V0,M1} { apart_point_and_line( skol3, line_connecting(
% 0.70/1.08 skol1, skol2 ) ) }.
% 0.70/1.08 (204) {G0,W6,D2,L2,V0,M2} { ! distinct_points( skol3, skol1 ), !
% 0.70/1.08 distinct_points( skol3, skol2 ) }.
% 0.70/1.08
% 0.70/1.08
% 0.70/1.08 Total Proof:
% 0.70/1.08
% 0.70/1.08 subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.70/1.08 parent0: (155) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.70/1.08 substitution0:
% 0.70/1.08 X := X
% 0.70/1.08 end
% 0.70/1.08 permutation0:
% 0.70/1.08 0 ==> 0
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 0.70/1.08 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 0.70/1.08 parent0: (158) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ),
% 0.70/1.08 distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 0.70/1.08 substitution0:
% 0.70/1.08 X := X
% 0.70/1.08 Y := Y
% 0.70/1.08 Z := Z
% 0.70/1.08 end
% 0.70/1.08 permutation0:
% 0.70/1.08 0 ==> 2
% 0.70/1.08 1 ==> 0
% 0.70/1.08 2 ==> 1
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 subsumption: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 0.70/1.08 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.70/1.08 parent0: (166) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 0.70/1.08 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 0.70/1.08 substitution0:
% 0.70/1.08 X := X
% 0.70/1.08 Y := Y
% 0.70/1.08 Z := Z
% 0.70/1.08 end
% 0.70/1.08 permutation0:
% 0.70/1.08 0 ==> 2
% 0.70/1.08 1 ==> 0
% 0.70/1.08 2 ==> 1
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 subsumption: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 0.70/1.08 distinct_lines( X, Y ) }.
% 0.70/1.08 parent0: (168) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ),
% 0.70/1.08 convergent_lines( X, Y ) }.
% 0.70/1.08 substitution0:
% 0.70/1.08 X := X
% 0.70/1.08 Y := Y
% 0.70/1.08 end
% 0.70/1.08 permutation0:
% 0.70/1.08 0 ==> 1
% 0.70/1.08 1 ==> 0
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 subsumption: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 0.70/1.08 parallel_through_point( Y, X ), Y ) }.
% 0.70/1.08 parent0: (169) {G0,W5,D3,L1,V2,M1} { ! convergent_lines(
% 0.70/1.08 parallel_through_point( Y, X ), Y ) }.
% 0.70/1.08 substitution0:
% 0.70/1.08 X := X
% 0.70/1.08 Y := Y
% 0.70/1.08 end
% 0.70/1.08 permutation0:
% 0.70/1.08 0 ==> 0
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 subsumption: (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.70/1.08 parallel_through_point( Y, X ) ) }.
% 0.70/1.08 parent0: (170) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.70/1.08 parallel_through_point( Y, X ) ) }.
% 0.70/1.08 substitution0:
% 0.70/1.08 X := X
% 0.70/1.08 Y := Y
% 0.70/1.08 end
% 0.70/1.08 permutation0:
% 0.70/1.08 0 ==> 0
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 subsumption: (47) {G0,W5,D3,L1,V0,M1} I { apart_point_and_line( skol3,
% 0.70/1.08 line_connecting( skol1, skol2 ) ) }.
% 0.70/1.08 parent0: (203) {G0,W5,D3,L1,V0,M1} { apart_point_and_line( skol3,
% 0.70/1.08 line_connecting( skol1, skol2 ) ) }.
% 0.70/1.08 substitution0:
% 0.70/1.08 end
% 0.70/1.08 permutation0:
% 0.70/1.08 0 ==> 0
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 resolution: (258) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 0.70/1.08 distinct_lines( X, Y ) }.
% 0.70/1.08 parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.70/1.08 parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 0.70/1.08 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 0.70/1.08 substitution0:
% 0.70/1.08 X := X
% 0.70/1.08 end
% 0.70/1.08 substitution1:
% 0.70/1.08 X := X
% 0.70/1.08 Y := Y
% 0.70/1.08 Z := X
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 subsumption: (55) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 0.70/1.08 distinct_lines( X, Y ) }.
% 0.70/1.08 parent0: (258) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 0.70/1.08 distinct_lines( X, Y ) }.
% 0.70/1.08 substitution0:
% 0.70/1.08 X := Y
% 0.70/1.08 Y := X
% 0.70/1.08 end
% 0.70/1.08 permutation0:
% 0.70/1.08 0 ==> 1
% 0.70/1.08 1 ==> 0
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 resolution: (260) {G1,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), !
% 0.70/1.08 distinct_lines( Y, X ) }.
% 0.70/1.08 parent0[1]: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 0.70/1.08 distinct_lines( X, Y ) }.
% 0.70/1.08 parent1[1]: (55) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 0.70/1.08 distinct_lines( X, Y ) }.
% 0.70/1.08 substitution0:
% 0.70/1.08 X := X
% 0.70/1.08 Y := Y
% 0.70/1.08 end
% 0.70/1.08 substitution1:
% 0.70/1.08 X := X
% 0.70/1.08 Y := Y
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 subsumption: (102) {G2,W6,D2,L2,V2,M1} R(14,55) { convergent_lines( X, Y )
% 0.70/1.08 , ! distinct_lines( Y, X ) }.
% 0.70/1.08 parent0: (260) {G1,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), !
% 0.70/1.08 distinct_lines( Y, X ) }.
% 0.70/1.08 substitution0:
% 0.70/1.08 X := X
% 0.70/1.08 Y := Y
% 0.70/1.08 end
% 0.70/1.08 permutation0:
% 0.70/1.08 0 ==> 0
% 0.70/1.08 1 ==> 1
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 resolution: (261) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 0.70/1.08 parallel_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 0.70/1.08 parent0[0]: (16) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 0.70/1.08 parallel_through_point( Y, X ) ) }.
% 0.70/1.08 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 0.70/1.08 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 0.70/1.08 substitution0:
% 0.70/1.08 X := X
% 0.70/1.08 Y := Y
% 0.70/1.08 end
% 0.70/1.08 substitution1:
% 0.70/1.08 X := X
% 0.70/1.08 Y := Z
% 0.70/1.08 Z := parallel_through_point( Y, X )
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 subsumption: (142) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X,
% 0.70/1.08 parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.70/1.08 parent0: (261) {G1,W8,D3,L2,V3,M2} { distinct_lines( Z,
% 0.70/1.08 parallel_through_point( Y, X ) ), ! apart_point_and_line( X, Z ) }.
% 0.70/1.08 substitution0:
% 0.70/1.08 X := Z
% 0.70/1.08 Y := Y
% 0.70/1.08 Z := X
% 0.70/1.08 end
% 0.70/1.08 permutation0:
% 0.70/1.08 0 ==> 0
% 0.70/1.08 1 ==> 1
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 resolution: (262) {G1,W7,D3,L1,V1,M1} { distinct_lines( line_connecting(
% 0.70/1.08 skol1, skol2 ), parallel_through_point( X, skol3 ) ) }.
% 0.70/1.08 parent0[1]: (142) {G1,W8,D3,L2,V3,M1} R(12,16) { distinct_lines( X,
% 0.70/1.08 parallel_through_point( Y, Z ) ), ! apart_point_and_line( Z, X ) }.
% 0.70/1.08 parent1[0]: (47) {G0,W5,D3,L1,V0,M1} I { apart_point_and_line( skol3,
% 0.70/1.08 line_connecting( skol1, skol2 ) ) }.
% 0.70/1.08 substitution0:
% 0.70/1.08 X := line_connecting( skol1, skol2 )
% 0.70/1.08 Y := X
% 0.70/1.08 Z := skol3
% 0.70/1.08 end
% 0.70/1.08 substitution1:
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 subsumption: (146) {G2,W7,D3,L1,V1,M1} R(142,47) { distinct_lines(
% 0.70/1.08 line_connecting( skol1, skol2 ), parallel_through_point( X, skol3 ) ) }.
% 0.70/1.08 parent0: (262) {G1,W7,D3,L1,V1,M1} { distinct_lines( line_connecting(
% 0.70/1.08 skol1, skol2 ), parallel_through_point( X, skol3 ) ) }.
% 0.70/1.08 substitution0:
% 0.70/1.08 X := X
% 0.70/1.08 end
% 0.70/1.08 permutation0:
% 0.70/1.08 0 ==> 0
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 resolution: (263) {G3,W7,D3,L1,V1,M1} { convergent_lines(
% 0.70/1.08 parallel_through_point( X, skol3 ), line_connecting( skol1, skol2 ) ) }.
% 0.70/1.08 parent0[1]: (102) {G2,W6,D2,L2,V2,M1} R(14,55) { convergent_lines( X, Y ),
% 0.70/1.08 ! distinct_lines( Y, X ) }.
% 0.70/1.08 parent1[0]: (146) {G2,W7,D3,L1,V1,M1} R(142,47) { distinct_lines(
% 0.70/1.08 line_connecting( skol1, skol2 ), parallel_through_point( X, skol3 ) ) }.
% 0.70/1.08 substitution0:
% 0.70/1.08 X := parallel_through_point( X, skol3 )
% 0.70/1.08 Y := line_connecting( skol1, skol2 )
% 0.70/1.08 end
% 0.70/1.08 substitution1:
% 0.70/1.08 X := X
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 subsumption: (147) {G3,W7,D3,L1,V1,M1} R(146,102) { convergent_lines(
% 0.70/1.08 parallel_through_point( X, skol3 ), line_connecting( skol1, skol2 ) ) }.
% 0.70/1.08 parent0: (263) {G3,W7,D3,L1,V1,M1} { convergent_lines(
% 0.70/1.08 parallel_through_point( X, skol3 ), line_connecting( skol1, skol2 ) ) }.
% 0.70/1.08 substitution0:
% 0.70/1.08 X := X
% 0.70/1.08 end
% 0.70/1.08 permutation0:
% 0.70/1.08 0 ==> 0
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 resolution: (264) {G1,W0,D0,L0,V0,M0} { }.
% 0.70/1.08 parent0[0]: (15) {G0,W5,D3,L1,V2,M1} I { ! convergent_lines(
% 0.70/1.08 parallel_through_point( Y, X ), Y ) }.
% 0.70/1.08 parent1[0]: (147) {G3,W7,D3,L1,V1,M1} R(146,102) { convergent_lines(
% 0.70/1.08 parallel_through_point( X, skol3 ), line_connecting( skol1, skol2 ) ) }.
% 0.70/1.08 substitution0:
% 0.70/1.08 X := skol3
% 0.70/1.08 Y := line_connecting( skol1, skol2 )
% 0.70/1.08 end
% 0.70/1.08 substitution1:
% 0.70/1.08 X := line_connecting( skol1, skol2 )
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 subsumption: (152) {G4,W0,D0,L0,V0,M0} R(147,15) { }.
% 0.70/1.08 parent0: (264) {G1,W0,D0,L0,V0,M0} { }.
% 0.70/1.08 substitution0:
% 0.70/1.08 end
% 0.70/1.08 permutation0:
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 Proof check complete!
% 0.70/1.08
% 0.70/1.08 Memory use:
% 0.70/1.08
% 0.70/1.08 space for terms: 3073
% 0.70/1.08 space for clauses: 7213
% 0.70/1.08
% 0.70/1.08
% 0.70/1.08 clauses generated: 392
% 0.70/1.08 clauses kept: 153
% 0.70/1.08 clauses selected: 54
% 0.70/1.08 clauses deleted: 0
% 0.70/1.08 clauses inuse deleted: 0
% 0.70/1.08
% 0.70/1.08 subsentry: 660
% 0.70/1.08 literals s-matched: 507
% 0.70/1.08 literals matched: 482
% 0.70/1.08 full subsumption: 176
% 0.70/1.08
% 0.70/1.08 checksum: 674612640
% 0.70/1.08
% 0.70/1.08
% 0.70/1.08 Bliksem ended
%------------------------------------------------------------------------------