TSTP Solution File: GEO208+3 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO208+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n015.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 02:52:45 EDT 2022
% Result : Theorem 0.44s 1.11s
% Output : Refutation 0.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO208+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Fri Jun 17 22:32:58 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.44/1.11 *** allocated 10000 integers for termspace/termends
% 0.44/1.11 *** allocated 10000 integers for clauses
% 0.44/1.11 *** allocated 10000 integers for justifications
% 0.44/1.11 Bliksem 1.12
% 0.44/1.11
% 0.44/1.11
% 0.44/1.11 Automatic Strategy Selection
% 0.44/1.11
% 0.44/1.11
% 0.44/1.11 Clauses:
% 0.44/1.11
% 0.44/1.11 { ! distinct_points( X, X ) }.
% 0.44/1.11 { ! distinct_lines( X, X ) }.
% 0.44/1.11 { ! convergent_lines( X, X ) }.
% 0.44/1.11 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 0.44/1.11 ) }.
% 0.44/1.11 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.44/1.11 }.
% 0.44/1.11 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 0.44/1.11 , Z ) }.
% 0.44/1.11 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 0.44/1.11 , Y ) ) }.
% 0.44/1.11 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 0.44/1.11 , Y ) ) }.
% 0.44/1.11 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.44/1.11 , Y ), X ) }.
% 0.44/1.11 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.44/1.11 , Y ), Y ) }.
% 0.44/1.11 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 0.44/1.11 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 0.44/1.11 apart_point_and_line( Y, T ) }.
% 0.44/1.11 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 0.44/1.11 apart_point_and_line( Z, Y ) }.
% 0.44/1.11 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 0.44/1.11 apart_point_and_line( X, Z ) }.
% 0.44/1.11 { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X,
% 0.44/1.11 Z ) }.
% 0.44/1.11 { ! distinct_lines( X, Y ), convergent_lines( X, Y ) }.
% 0.44/1.11 { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 0.44/1.11 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 0.44/1.11 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 0.44/1.11 apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 0.44/1.11 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.44/1.11 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.44/1.11 , convergent_lines( Y, Z ) }.
% 0.44/1.11 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.44/1.11 , unorthogonal_lines( Y, Z ) }.
% 0.44/1.11 { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 0.44/1.11 { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.44/1.11 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 0.44/1.11 }.
% 0.44/1.11 { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 0.44/1.11 { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 0.44/1.11 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 0.44/1.11 apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ),
% 0.44/1.11 unorthogonal_lines( Y, T ) }.
% 0.44/1.11 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.44/1.11 { alpha2( X, Z ), convergent_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 0.44/1.11 unorthogonal_lines( X, Y ) }.
% 0.44/1.11 { alpha2( X, Z ), unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 0.44/1.11 unorthogonal_lines( X, Y ) }.
% 0.44/1.11 { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 0.44/1.11 { ! alpha2( X, Y ), unorthogonal_lines( Y, X ) }.
% 0.44/1.11 { ! convergent_lines( Y, X ), ! unorthogonal_lines( Y, X ), alpha2( X, Y )
% 0.44/1.11 }.
% 0.44/1.11 { unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ), !
% 0.44/1.11 convergent_lines( X, Y ) }.
% 0.44/1.11 { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line(
% 0.44/1.11 line_connecting( X, Y ) ) }.
% 0.44/1.11 { ! line( X ), ! line( Y ), ! convergent_lines( X, Y ), point(
% 0.44/1.11 intersection_point( X, Y ) ) }.
% 0.44/1.11 { ! line( X ), ! point( Y ), line( parallel_through_point( X, Y ) ) }.
% 0.44/1.11 { ! line( X ), ! point( Y ), line( orthogonal_through_point( X, Y ) ) }.
% 0.44/1.11 { ! equal_points( X, Y ), ! distinct_points( X, Y ) }.
% 0.44/1.11 { distinct_points( X, Y ), equal_points( X, Y ) }.
% 0.44/1.11 { ! equal_lines( X, Y ), ! distinct_lines( X, Y ) }.
% 0.44/1.11 { distinct_lines( X, Y ), equal_lines( X, Y ) }.
% 0.44/1.11 { ! parallel_lines( X, Y ), ! convergent_lines( X, Y ) }.
% 0.44/1.11 { convergent_lines( X, Y ), parallel_lines( X, Y ) }.
% 0.44/1.11 { ! incident_point_and_line( X, Y ), ! apart_point_and_line( X, Y ) }.
% 0.44/1.11 { apart_point_and_line( X, Y ), incident_point_and_line( X, Y ) }.
% 0.44/1.11 { ! orthogonal_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.44/1.11 { unorthogonal_lines( X, Y ), orthogonal_lines( X, Y ) }.
% 0.44/1.11 { incident_point_and_line( skol3, skol1 ) }.
% 0.44/1.11 { incident_point_and_line( skol3, skol2 ) }.
% 0.44/1.11 { parallel_lines( skol1, skol2 ) }.
% 0.44/1.11 { ! equal_lines( skol1, skol2 ) }.
% 0.44/1.11
% 0.44/1.11 percentage equality = 0.000000, percentage horn = 0.620000
% 0.44/1.11 This a non-horn, non-equality problem
% 0.44/1.11
% 0.44/1.11
% 0.44/1.11 Options Used:
% 0.44/1.11
% 0.44/1.11 useres = 1
% 0.44/1.11 useparamod = 0
% 0.44/1.11 useeqrefl = 0
% 0.44/1.11 useeqfact = 0
% 0.44/1.11 usefactor = 1
% 0.44/1.11 usesimpsplitting = 0
% 0.44/1.11 usesimpdemod = 0
% 0.44/1.11 usesimpres = 3
% 0.44/1.11
% 0.44/1.11 resimpinuse = 1000
% 0.44/1.11 resimpclauses = 20000
% 0.44/1.11 substype = standard
% 0.44/1.11 backwardsubs = 1
% 0.44/1.11 selectoldest = 5
% 0.44/1.11
% 0.44/1.11 litorderings [0] = split
% 0.44/1.11 litorderings [1] = liftord
% 0.44/1.11
% 0.44/1.11 termordering = none
% 0.44/1.11
% 0.44/1.11 litapriori = 1
% 0.44/1.11 termapriori = 0
% 0.44/1.11 litaposteriori = 0
% 0.44/1.11 termaposteriori = 0
% 0.44/1.11 demodaposteriori = 0
% 0.44/1.11 ordereqreflfact = 0
% 0.44/1.11
% 0.44/1.11 litselect = none
% 0.44/1.11
% 0.44/1.11 maxweight = 15
% 0.44/1.11 maxdepth = 30000
% 0.44/1.11 maxlength = 115
% 0.44/1.11 maxnrvars = 195
% 0.44/1.11 excuselevel = 1
% 0.44/1.11 increasemaxweight = 1
% 0.44/1.11
% 0.44/1.11 maxselected = 10000000
% 0.44/1.11 maxnrclauses = 10000000
% 0.44/1.11
% 0.44/1.11 showgenerated = 0
% 0.44/1.11 showkept = 0
% 0.44/1.11 showselected = 0
% 0.44/1.11 showdeleted = 0
% 0.44/1.11 showresimp = 1
% 0.44/1.11 showstatus = 2000
% 0.44/1.11
% 0.44/1.11 prologoutput = 0
% 0.44/1.11 nrgoals = 5000000
% 0.44/1.11 totalproof = 1
% 0.44/1.11
% 0.44/1.11 Symbols occurring in the translation:
% 0.44/1.11
% 0.44/1.11 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.44/1.11 . [1, 2] (w:1, o:26, a:1, s:1, b:0),
% 0.44/1.11 ! [4, 1] (w:0, o:19, a:1, s:1, b:0),
% 0.44/1.11 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.44/1.11 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.44/1.11 distinct_points [36, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.44/1.11 distinct_lines [37, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.44/1.11 convergent_lines [38, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.44/1.11 line_connecting [41, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.44/1.11 apart_point_and_line [42, 2] (w:1, o:54, a:1, s:1, b:0),
% 0.44/1.11 intersection_point [43, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.44/1.11 parallel_through_point [46, 2] (w:1, o:58, a:1, s:1, b:0),
% 0.44/1.11 unorthogonal_lines [49, 2] (w:1, o:59, a:1, s:1, b:0),
% 0.44/1.11 orthogonal_through_point [52, 2] (w:1, o:56, a:1, s:1, b:0),
% 0.44/1.11 point [54, 1] (w:1, o:24, a:1, s:1, b:0),
% 0.44/1.11 line [55, 1] (w:1, o:25, a:1, s:1, b:0),
% 0.44/1.11 equal_points [56, 2] (w:1, o:60, a:1, s:1, b:0),
% 0.44/1.11 equal_lines [57, 2] (w:1, o:61, a:1, s:1, b:0),
% 0.44/1.11 parallel_lines [58, 2] (w:1, o:62, a:1, s:1, b:0),
% 0.44/1.11 incident_point_and_line [59, 2] (w:1, o:63, a:1, s:1, b:0),
% 0.44/1.11 orthogonal_lines [60, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.44/1.11 alpha1 [61, 2] (w:1, o:64, a:1, s:1, b:0),
% 0.44/1.11 alpha2 [62, 2] (w:1, o:65, a:1, s:1, b:0),
% 0.44/1.11 skol1 [63, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.44/1.11 skol2 [64, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.44/1.11 skol3 [65, 0] (w:1, o:18, a:1, s:1, b:0).
% 0.44/1.11
% 0.44/1.11
% 0.44/1.11 Starting Search:
% 0.44/1.11
% 0.44/1.11
% 0.44/1.11 Bliksems!, er is een bewijs:
% 0.44/1.11 % SZS status Theorem
% 0.44/1.11 % SZS output start Refutation
% 0.44/1.11
% 0.44/1.11 (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.44/1.11 (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.44/1.11 (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.44/1.11 , ! distinct_lines( X, Y ) }.
% 0.44/1.11 (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), convergent_lines( Y,
% 0.44/1.11 Z ), ! convergent_lines( X, Y ) }.
% 0.44/1.11 (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! distinct_lines( X
% 0.44/1.11 , Y ) }.
% 0.44/1.11 (39) {G0,W6,D2,L2,V2,M1} I { distinct_lines( X, Y ), equal_lines( X, Y )
% 0.44/1.11 }.
% 0.44/1.11 (40) {G0,W6,D2,L2,V2,M1} I { ! convergent_lines( X, Y ), ! parallel_lines(
% 0.44/1.11 X, Y ) }.
% 0.44/1.11 (48) {G0,W3,D2,L1,V0,M1} I { parallel_lines( skol1, skol2 ) }.
% 0.44/1.11 (49) {G0,W3,D2,L1,V0,M1} I { ! equal_lines( skol1, skol2 ) }.
% 0.44/1.11 (55) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 0.44/1.11 ( X, Y ) }.
% 0.44/1.11 (64) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.44/1.11 convergent_lines( X, Y ) }.
% 0.44/1.11 (73) {G1,W3,D2,L1,V0,M1} R(40,48) { ! convergent_lines( skol1, skol2 ) }.
% 0.44/1.11 (74) {G2,W3,D2,L1,V0,M1} R(73,64) { ! convergent_lines( skol2, skol1 ) }.
% 0.44/1.11 (79) {G1,W3,D2,L1,V0,M1} R(39,49) { distinct_lines( skol1, skol2 ) }.
% 0.44/1.11 (80) {G2,W3,D2,L1,V0,M1} R(79,55) { distinct_lines( skol2, skol1 ) }.
% 0.44/1.11 (133) {G3,W0,D0,L0,V0,M0} R(14,80);r(74) { }.
% 0.44/1.11
% 0.44/1.11
% 0.44/1.11 % SZS output end Refutation
% 0.44/1.11 found a proof!
% 0.44/1.11
% 0.44/1.11
% 0.44/1.11 Unprocessed initial clauses:
% 0.44/1.11
% 0.44/1.11 (135) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 0.44/1.11 (136) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.44/1.11 (137) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 0.44/1.11 (138) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 0.44/1.11 , Z ), distinct_points( Y, Z ) }.
% 0.44/1.11 (139) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X, Z
% 0.44/1.11 ), distinct_lines( Y, Z ) }.
% 0.44/1.11 (140) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines(
% 0.44/1.11 X, Z ), convergent_lines( Y, Z ) }.
% 0.44/1.11 (141) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.44/1.11 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 0.44/1.11 (142) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.44/1.11 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 0.44/1.11 (143) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 0.44/1.11 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 0.44/1.11 (144) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 0.44/1.11 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 0.44/1.11 (145) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines(
% 0.44/1.11 Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 0.44/1.11 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 0.44/1.11 (146) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 0.44/1.11 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 0.44/1.11 (147) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ), distinct_lines
% 0.44/1.11 ( Y, Z ), apart_point_and_line( X, Z ) }.
% 0.44/1.11 (148) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), distinct_lines( Y
% 0.44/1.11 , Z ), convergent_lines( X, Z ) }.
% 0.44/1.11 (149) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ), convergent_lines( X
% 0.44/1.11 , Y ) }.
% 0.44/1.11 (150) {G0,W5,D3,L1,V2,M1} { ! convergent_lines( parallel_through_point( Y
% 0.44/1.11 , X ), Y ) }.
% 0.44/1.11 (151) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.44/1.11 parallel_through_point( Y, X ) ) }.
% 0.44/1.11 (152) {G0,W12,D2,L4,V3,M4} { ! distinct_lines( X, Y ),
% 0.44/1.11 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 0.44/1.11 convergent_lines( X, Y ) }.
% 0.44/1.11 (153) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines(
% 0.44/1.11 X, Y ) }.
% 0.44/1.11 (154) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.44/1.11 unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 0.44/1.11 (155) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.44/1.11 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 0.44/1.11 }.
% 0.44/1.11 (156) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 0.44/1.11 (157) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 0.44/1.11 }.
% 0.44/1.11 (158) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( X, Y ), !
% 0.44/1.11 unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 0.44/1.11 (159) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines( orthogonal_through_point
% 0.44/1.11 ( Y, X ), Y ) }.
% 0.44/1.11 (160) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.44/1.11 orthogonal_through_point( Y, X ) ) }.
% 0.44/1.11 (161) {G0,W15,D2,L5,V4,M5} { ! distinct_lines( X, Y ),
% 0.44/1.11 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 0.44/1.11 unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 0.44/1.11 (162) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines(
% 0.44/1.11 X, Y ) }.
% 0.44/1.11 (163) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), convergent_lines( Z, Y ), !
% 0.44/1.11 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.44/1.11 (164) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), unorthogonal_lines( Z, Y ), !
% 0.44/1.11 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.44/1.11 (165) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 0.44/1.11 (166) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), unorthogonal_lines( Y, X )
% 0.44/1.11 }.
% 0.44/1.11 (167) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( Y, X ), !
% 0.44/1.11 unorthogonal_lines( Y, X ), alpha2( X, Y ) }.
% 0.44/1.11 (168) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ), unorthogonal_lines
% 0.44/1.11 ( Z, Y ), ! convergent_lines( X, Y ) }.
% 0.44/1.11 (169) {G0,W11,D3,L4,V2,M4} { ! point( X ), ! point( Y ), ! distinct_points
% 0.44/1.11 ( X, Y ), line( line_connecting( X, Y ) ) }.
% 0.44/1.11 (170) {G0,W11,D3,L4,V2,M4} { ! line( X ), ! line( Y ), ! convergent_lines
% 0.44/1.11 ( X, Y ), point( intersection_point( X, Y ) ) }.
% 0.44/1.11 (171) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 0.44/1.11 parallel_through_point( X, Y ) ) }.
% 0.44/1.11 (172) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 0.44/1.11 orthogonal_through_point( X, Y ) ) }.
% 0.44/1.11 (173) {G0,W6,D2,L2,V2,M2} { ! equal_points( X, Y ), ! distinct_points( X,
% 0.44/1.11 Y ) }.
% 0.44/1.11 (174) {G0,W6,D2,L2,V2,M2} { distinct_points( X, Y ), equal_points( X, Y )
% 0.44/1.11 }.
% 0.44/1.11 (175) {G0,W6,D2,L2,V2,M2} { ! equal_lines( X, Y ), ! distinct_lines( X, Y
% 0.44/1.11 ) }.
% 0.44/1.11 (176) {G0,W6,D2,L2,V2,M2} { distinct_lines( X, Y ), equal_lines( X, Y )
% 0.44/1.11 }.
% 0.44/1.11 (177) {G0,W6,D2,L2,V2,M2} { ! parallel_lines( X, Y ), ! convergent_lines(
% 0.44/1.11 X, Y ) }.
% 0.44/1.11 (178) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), parallel_lines( X, Y
% 0.44/1.11 ) }.
% 0.44/1.11 (179) {G0,W6,D2,L2,V2,M2} { ! incident_point_and_line( X, Y ), !
% 0.44/1.11 apart_point_and_line( X, Y ) }.
% 0.44/1.11 (180) {G0,W6,D2,L2,V2,M2} { apart_point_and_line( X, Y ),
% 0.44/1.11 incident_point_and_line( X, Y ) }.
% 0.44/1.11 (181) {G0,W6,D2,L2,V2,M2} { ! orthogonal_lines( X, Y ), !
% 0.44/1.11 unorthogonal_lines( X, Y ) }.
% 0.44/1.11 (182) {G0,W6,D2,L2,V2,M2} { unorthogonal_lines( X, Y ), orthogonal_lines(
% 0.44/1.11 X, Y ) }.
% 0.44/1.11 (183) {G0,W3,D2,L1,V0,M1} { incident_point_and_line( skol3, skol1 ) }.
% 0.44/1.11 (184) {G0,W3,D2,L1,V0,M1} { incident_point_and_line( skol3, skol2 ) }.
% 0.44/1.11 (185) {G0,W3,D2,L1,V0,M1} { parallel_lines( skol1, skol2 ) }.
% 0.44/1.11 (186) {G0,W3,D2,L1,V0,M1} { ! equal_lines( skol1, skol2 ) }.
% 0.44/1.11
% 0.44/1.11
% 0.44/1.11 Total Proof:
% 0.44/1.11
% 0.44/1.11 subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.44/1.11 parent0: (136) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.44/1.11 substitution0:
% 0.44/1.11 X := X
% 0.44/1.11 end
% 0.44/1.11 permutation0:
% 0.44/1.11 0 ==> 0
% 0.44/1.11 end
% 0.44/1.11
% 0.44/1.11 subsumption: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.44/1.11 parent0: (137) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 0.44/1.11 substitution0:
% 0.44/1.11 X := X
% 0.44/1.11 end
% 0.44/1.11 permutation0:
% 0.44/1.11 0 ==> 0
% 0.44/1.11 end
% 0.44/1.11
% 0.44/1.11 subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 0.44/1.11 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 0.44/1.11 parent0: (139) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ),
% 0.44/1.11 distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 0.44/1.11 substitution0:
% 0.44/1.11 X := X
% 0.44/1.11 Y := Y
% 0.44/1.11 Z := Z
% 0.44/1.11 end
% 0.44/1.11 permutation0:
% 0.44/1.11 0 ==> 2
% 0.44/1.11 1 ==> 0
% 0.44/1.11 2 ==> 1
% 0.44/1.11 end
% 0.44/1.11
% 0.44/1.11 subsumption: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 0.44/1.11 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.44/1.11 parent0: (140) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 0.44/1.11 convergent_lines( X, Z ), convergent_lines( Y, Z ) }.
% 0.44/1.11 substitution0:
% 0.44/1.11 X := X
% 0.44/1.11 Y := Y
% 0.44/1.11 Z := Z
% 0.44/1.11 end
% 0.44/1.11 permutation0:
% 0.44/1.11 0 ==> 2
% 0.44/1.11 1 ==> 0
% 0.44/1.11 2 ==> 1
% 0.44/1.11 end
% 0.44/1.11
% 0.44/1.11 subsumption: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 0.44/1.11 distinct_lines( X, Y ) }.
% 0.44/1.11 parent0: (149) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ),
% 0.44/1.11 convergent_lines( X, Y ) }.
% 0.44/1.11 substitution0:
% 0.44/1.11 X := X
% 0.44/1.11 Y := Y
% 0.44/1.11 end
% 0.44/1.11 permutation0:
% 0.44/1.11 0 ==> 1
% 0.44/1.11 1 ==> 0
% 0.44/1.11 end
% 0.44/1.11
% 0.44/1.11 subsumption: (39) {G0,W6,D2,L2,V2,M1} I { distinct_lines( X, Y ),
% 0.44/1.11 equal_lines( X, Y ) }.
% 0.44/1.11 parent0: (176) {G0,W6,D2,L2,V2,M2} { distinct_lines( X, Y ), equal_lines(
% 0.44/1.11 X, Y ) }.
% 0.44/1.11 substitution0:
% 0.44/1.11 X := X
% 0.44/1.11 Y := Y
% 0.44/1.11 end
% 0.44/1.11 permutation0:
% 0.44/1.11 0 ==> 0
% 0.44/1.11 1 ==> 1
% 0.44/1.11 end
% 0.44/1.11
% 0.44/1.11 subsumption: (40) {G0,W6,D2,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 0.44/1.11 parallel_lines( X, Y ) }.
% 0.44/1.11 parent0: (177) {G0,W6,D2,L2,V2,M2} { ! parallel_lines( X, Y ), !
% 0.44/1.11 convergent_lines( X, Y ) }.
% 0.44/1.11 substitution0:
% 0.44/1.11 X := X
% 0.44/1.11 Y := Y
% 0.44/1.11 end
% 0.44/1.11 permutation0:
% 0.44/1.11 0 ==> 1
% 0.44/1.11 1 ==> 0
% 0.44/1.11 end
% 0.44/1.11
% 0.44/1.11 subsumption: (48) {G0,W3,D2,L1,V0,M1} I { parallel_lines( skol1, skol2 )
% 0.44/1.11 }.
% 0.44/1.11 parent0: (185) {G0,W3,D2,L1,V0,M1} { parallel_lines( skol1, skol2 ) }.
% 0.44/1.11 substitution0:
% 0.44/1.11 end
% 0.44/1.11 permutation0:
% 0.44/1.11 0 ==> 0
% 0.44/1.11 end
% 0.44/1.11
% 0.44/1.11 subsumption: (49) {G0,W3,D2,L1,V0,M1} I { ! equal_lines( skol1, skol2 ) }.
% 0.44/1.11 parent0: (186) {G0,W3,D2,L1,V0,M1} { ! equal_lines( skol1, skol2 ) }.
% 0.44/1.11 substitution0:
% 0.44/1.11 end
% 0.44/1.11 permutation0:
% 0.44/1.11 0 ==> 0
% 0.44/1.11 end
% 0.44/1.11
% 0.44/1.11 resolution: (261) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 0.44/1.11 distinct_lines( X, Y ) }.
% 0.44/1.11 parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 0.44/1.11 parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 0.44/1.11 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 0.44/1.11 substitution0:
% 0.44/1.11 X := X
% 0.44/1.11 end
% 0.44/1.11 substitution1:
% 0.44/1.11 X := X
% 0.44/1.11 Y := Y
% 0.44/1.11 Z := X
% 0.44/1.11 end
% 0.44/1.11
% 0.44/1.11 subsumption: (55) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 0.44/1.11 distinct_lines( X, Y ) }.
% 0.44/1.11 parent0: (261) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 0.44/1.11 distinct_lines( X, Y ) }.
% 0.44/1.11 substitution0:
% 0.44/1.11 X := Y
% 0.44/1.11 Y := X
% 0.44/1.11 end
% 0.44/1.11 permutation0:
% 0.44/1.11 0 ==> 1
% 0.44/1.11 1 ==> 0
% 0.44/1.11 end
% 0.44/1.11
% 0.44/1.11 resolution: (263) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 0.44/1.11 convergent_lines( X, Y ) }.
% 0.44/1.11 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.44/1.11 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 0.44/1.11 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.44/1.11 substitution0:
% 0.44/1.11 X := X
% 0.44/1.11 end
% 0.44/1.11 substitution1:
% 0.44/1.11 X := X
% 0.44/1.11 Y := Y
% 0.44/1.11 Z := X
% 0.44/1.11 end
% 0.44/1.11
% 0.44/1.11 subsumption: (64) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.44/1.11 convergent_lines( X, Y ) }.
% 0.44/1.11 parent0: (263) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 0.44/1.11 convergent_lines( X, Y ) }.
% 0.44/1.11 substitution0:
% 0.44/1.11 X := Y
% 0.44/1.11 Y := X
% 0.44/1.11 end
% 0.44/1.11 permutation0:
% 0.44/1.11 0 ==> 1
% 0.44/1.11 1 ==> 0
% 0.44/1.11 end
% 0.44/1.11
% 0.44/1.11 resolution: (265) {G1,W3,D2,L1,V0,M1} { ! convergent_lines( skol1, skol2 )
% 0.44/1.11 }.
% 0.44/1.11 parent0[1]: (40) {G0,W6,D2,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 0.44/1.11 parallel_lines( X, Y ) }.
% 0.44/1.11 parent1[0]: (48) {G0,W3,D2,L1,V0,M1} I { parallel_lines( skol1, skol2 ) }.
% 0.44/1.11 substitution0:
% 0.44/1.11 X := skol1
% 0.44/1.11 Y := skol2
% 0.44/1.11 end
% 0.44/1.11 substitution1:
% 0.44/1.11 end
% 0.44/1.11
% 0.44/1.11 subsumption: (73) {G1,W3,D2,L1,V0,M1} R(40,48) { ! convergent_lines( skol1
% 0.44/1.11 , skol2 ) }.
% 0.44/1.11 parent0: (265) {G1,W3,D2,L1,V0,M1} { ! convergent_lines( skol1, skol2 )
% 0.44/1.11 }.
% 0.44/1.11 substitution0:
% 0.44/1.11 end
% 0.44/1.11 permutation0:
% 0.44/1.11 0 ==> 0
% 0.44/1.11 end
% 0.44/1.11
% 0.44/1.11 resolution: (266) {G2,W3,D2,L1,V0,M1} { ! convergent_lines( skol2, skol1 )
% 0.44/1.11 }.
% 0.44/1.11 parent0[0]: (73) {G1,W3,D2,L1,V0,M1} R(40,48) { ! convergent_lines( skol1,
% 0.44/1.11 skol2 ) }.
% 0.44/1.11 parent1[1]: (64) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.44/1.11 convergent_lines( X, Y ) }.
% 0.44/1.11 substitution0:
% 0.44/1.11 end
% 0.44/1.11 substitution1:
% 0.44/1.11 X := skol1
% 0.44/1.11 Y := skol2
% 0.44/1.11 end
% 0.44/1.11
% 0.44/1.11 subsumption: (74) {G2,W3,D2,L1,V0,M1} R(73,64) { ! convergent_lines( skol2
% 0.44/1.11 , skol1 ) }.
% 0.44/1.11 parent0: (266) {G2,W3,D2,L1,V0,M1} { ! convergent_lines( skol2, skol1 )
% 0.44/1.11 }.
% 0.44/1.11 substitution0:
% 0.44/1.11 end
% 0.44/1.11 permutation0:
% 0.44/1.11 0 ==> 0
% 0.44/1.11 end
% 0.44/1.11
% 0.44/1.11 resolution: (267) {G1,W3,D2,L1,V0,M1} { distinct_lines( skol1, skol2 ) }.
% 0.44/1.11 parent0[0]: (49) {G0,W3,D2,L1,V0,M1} I { ! equal_lines( skol1, skol2 ) }.
% 0.44/1.11 parent1[1]: (39) {G0,W6,D2,L2,V2,M1} I { distinct_lines( X, Y ),
% 0.44/1.11 equal_lines( X, Y ) }.
% 0.44/1.11 substitution0:
% 0.44/1.11 end
% 0.44/1.11 substitution1:
% 0.44/1.11 X := skol1
% 0.44/1.11 Y := skol2
% 0.44/1.11 end
% 0.44/1.11
% 0.44/1.11 subsumption: (79) {G1,W3,D2,L1,V0,M1} R(39,49) { distinct_lines( skol1,
% 0.44/1.11 skol2 ) }.
% 0.44/1.11 parent0: (267) {G1,W3,D2,L1,V0,M1} { distinct_lines( skol1, skol2 ) }.
% 0.44/1.11 substitution0:
% 0.44/1.11 end
% 0.44/1.11 permutation0:
% 0.44/1.11 0 ==> 0
% 0.44/1.11 end
% 0.44/1.11
% 0.44/1.11 resolution: (268) {G2,W3,D2,L1,V0,M1} { distinct_lines( skol2, skol1 ) }.
% 0.44/1.11 parent0[0]: (55) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 0.44/1.11 distinct_lines( X, Y ) }.
% 0.44/1.11 parent1[0]: (79) {G1,W3,D2,L1,V0,M1} R(39,49) { distinct_lines( skol1,
% 0.44/1.11 skol2 ) }.
% 0.44/1.11 substitution0:
% 0.44/1.11 X := skol2
% 0.44/1.11 Y := skol1
% 0.44/1.11 end
% 0.44/1.11 substitution1:
% 0.44/1.11 end
% 0.44/1.11
% 0.44/1.11 subsumption: (80) {G2,W3,D2,L1,V0,M1} R(79,55) { distinct_lines( skol2,
% 0.44/1.11 skol1 ) }.
% 0.44/1.11 parent0: (268) {G2,W3,D2,L1,V0,M1} { distinct_lines( skol2, skol1 ) }.
% 0.44/1.11 substitution0:
% 0.44/1.11 end
% 0.44/1.11 permutation0:
% 0.44/1.11 0 ==> 0
% 0.44/1.11 end
% 0.44/1.11
% 0.44/1.11 resolution: (269) {G1,W3,D2,L1,V0,M1} { convergent_lines( skol2, skol1 )
% 0.44/1.11 }.
% 0.44/1.11 parent0[1]: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 0.44/1.11 distinct_lines( X, Y ) }.
% 0.44/1.11 parent1[0]: (80) {G2,W3,D2,L1,V0,M1} R(79,55) { distinct_lines( skol2,
% 0.44/1.11 skol1 ) }.
% 0.44/1.11 substitution0:
% 0.44/1.11 X := skol2
% 0.44/1.11 Y := skol1
% 0.44/1.11 end
% 0.44/1.11 substitution1:
% 0.44/1.11 end
% 0.44/1.11
% 0.44/1.11 resolution: (270) {G2,W0,D0,L0,V0,M0} { }.
% 0.44/1.11 parent0[0]: (74) {G2,W3,D2,L1,V0,M1} R(73,64) { ! convergent_lines( skol2,
% 0.44/1.11 skol1 ) }.
% 0.44/1.11 parent1[0]: (269) {G1,W3,D2,L1,V0,M1} { convergent_lines( skol2, skol1 )
% 0.44/1.11 }.
% 0.44/1.11 substitution0:
% 0.44/1.11 end
% 0.44/1.11 substitution1:
% 0.44/1.11 end
% 0.44/1.11
% 0.44/1.11 subsumption: (133) {G3,W0,D0,L0,V0,M0} R(14,80);r(74) { }.
% 0.44/1.11 parent0: (270) {G2,W0,D0,L0,V0,M0} { }.
% 0.44/1.11 substitution0:
% 0.44/1.11 end
% 0.44/1.11 permutation0:
% 0.44/1.11 end
% 0.44/1.11
% 0.44/1.11 Proof check complete!
% 0.44/1.11
% 0.44/1.11 Memory use:
% 0.44/1.11
% 0.44/1.11 space for terms: 2834
% 0.44/1.11 space for clauses: 6213
% 0.44/1.11
% 0.44/1.11
% 0.44/1.11 clauses generated: 337
% 0.44/1.11 clauses kept: 134
% 0.44/1.11 clauses selected: 50
% 0.44/1.11 clauses deleted: 0
% 0.44/1.11 clauses inuse deleted: 0
% 0.44/1.11
% 0.44/1.11 subsentry: 516
% 0.44/1.11 literals s-matched: 372
% 0.44/1.11 literals matched: 347
% 0.44/1.11 full subsumption: 125
% 0.44/1.11
% 0.44/1.11 checksum: -1345635251
% 0.44/1.11
% 0.44/1.11
% 0.44/1.11 Bliksem ended
%------------------------------------------------------------------------------