TSTP Solution File: GEO233+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO233+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Sat Jul 16 02:53:06 EDT 2022
% Result : Theorem 0.42s 1.17s
% Output : Refutation 0.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO233+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.07/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n006.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 : Sat Jun 18 13:37:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.42/1.16 *** allocated 10000 integers for termspace/termends
% 0.42/1.16 *** allocated 10000 integers for clauses
% 0.42/1.16 *** allocated 10000 integers for justifications
% 0.42/1.16 Bliksem 1.12
% 0.42/1.16
% 0.42/1.16
% 0.42/1.16 Automatic Strategy Selection
% 0.42/1.16
% 0.42/1.16
% 0.42/1.16 Clauses:
% 0.42/1.16
% 0.42/1.16 { ! apart_point_and_line( X, Y ), left_apart_point( X, Y ),
% 0.42/1.16 left_apart_point( X, reverse_line( Y ) ) }.
% 0.42/1.16 { ! left_apart_point( X, Y ), apart_point_and_line( X, Y ) }.
% 0.42/1.16 { ! left_apart_point( X, reverse_line( Y ) ), apart_point_and_line( X, Y )
% 0.42/1.16 }.
% 0.42/1.16 { ! convergent_lines( X, Y ), unequally_directed_lines( X, Y ) }.
% 0.42/1.16 { ! convergent_lines( X, Y ), unequally_directed_lines( X, reverse_line( Y
% 0.42/1.16 ) ) }.
% 0.42/1.16 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.42/1.16 reverse_line( Y ) ), convergent_lines( X, Y ) }.
% 0.42/1.16 { ! divides_points( Z, X, Y ), alpha1( X, Y, Z ), alpha4( X, Y, Z ) }.
% 0.42/1.16 { ! alpha1( X, Y, Z ), divides_points( Z, X, Y ) }.
% 0.42/1.16 { ! alpha4( X, Y, Z ), divides_points( Z, X, Y ) }.
% 0.42/1.16 { ! alpha4( X, Y, Z ), left_apart_point( X, reverse_line( Z ) ) }.
% 0.42/1.16 { ! alpha4( X, Y, Z ), left_apart_point( Y, Z ) }.
% 0.42/1.16 { ! left_apart_point( X, reverse_line( Z ) ), ! left_apart_point( Y, Z ),
% 0.42/1.16 alpha4( X, Y, Z ) }.
% 0.42/1.16 { ! alpha1( X, Y, Z ), left_apart_point( X, Z ) }.
% 0.42/1.16 { ! alpha1( X, Y, Z ), left_apart_point( Y, reverse_line( Z ) ) }.
% 0.42/1.16 { ! left_apart_point( X, Z ), ! left_apart_point( Y, reverse_line( Z ) ),
% 0.42/1.16 alpha1( X, Y, Z ) }.
% 0.42/1.16 { ! before_on_line( X, Y, Z ), distinct_points( Y, Z ) }.
% 0.42/1.16 { ! before_on_line( X, Y, Z ), alpha7( X, Y, Z ) }.
% 0.42/1.16 { ! distinct_points( Y, Z ), ! alpha7( X, Y, Z ), before_on_line( X, Y, Z )
% 0.42/1.16 }.
% 0.42/1.16 { ! alpha7( X, Y, Z ), alpha2( X, Y ) }.
% 0.42/1.16 { ! alpha7( X, Y, Z ), alpha8( X, Y, Z ) }.
% 0.42/1.16 { ! alpha2( X, Y ), ! alpha8( X, Y, Z ), alpha7( X, Y, Z ) }.
% 0.42/1.16 { ! alpha8( X, Y, Z ), alpha5( X, Z ) }.
% 0.42/1.16 { ! alpha8( X, Y, Z ), ! unequally_directed_lines( X, line_connecting( Y, Z
% 0.42/1.16 ) ) }.
% 0.42/1.16 { ! alpha5( X, Z ), unequally_directed_lines( X, line_connecting( Y, Z ) )
% 0.42/1.16 , alpha8( X, Y, Z ) }.
% 0.42/1.16 { ! alpha5( X, Y ), ! left_apart_point( Y, X ) }.
% 0.42/1.16 { ! alpha5( X, Y ), ! left_apart_point( Y, reverse_line( X ) ) }.
% 0.42/1.16 { left_apart_point( Y, X ), left_apart_point( Y, reverse_line( X ) ),
% 0.42/1.16 alpha5( X, Y ) }.
% 0.42/1.16 { ! alpha2( X, Y ), ! left_apart_point( Y, X ) }.
% 0.42/1.16 { ! alpha2( X, Y ), ! left_apart_point( Y, reverse_line( X ) ) }.
% 0.42/1.16 { left_apart_point( Y, X ), left_apart_point( Y, reverse_line( X ) ),
% 0.42/1.16 alpha2( X, Y ) }.
% 0.42/1.16 { ! between_on_line( X, Y, Z, T ), alpha3( X, Y, Z, T ), alpha6( X, Y, Z, T
% 0.42/1.16 ) }.
% 0.42/1.16 { ! alpha3( X, Y, Z, T ), between_on_line( X, Y, Z, T ) }.
% 0.42/1.16 { ! alpha6( X, Y, Z, T ), between_on_line( X, Y, Z, T ) }.
% 0.42/1.16 { ! alpha6( X, Y, Z, T ), before_on_line( X, T, Z ) }.
% 0.42/1.16 { ! alpha6( X, Y, Z, T ), before_on_line( X, Z, Y ) }.
% 0.42/1.16 { ! before_on_line( X, T, Z ), ! before_on_line( X, Z, Y ), alpha6( X, Y, Z
% 0.42/1.16 , T ) }.
% 0.42/1.16 { ! alpha3( X, Y, Z, T ), before_on_line( X, Y, Z ) }.
% 0.42/1.16 { ! alpha3( X, Y, Z, T ), before_on_line( X, Z, T ) }.
% 0.42/1.16 { ! before_on_line( X, Y, Z ), ! before_on_line( X, Z, T ), alpha3( X, Y, Z
% 0.42/1.16 , T ) }.
% 0.42/1.16 { ! distinct_points( X, X ) }.
% 0.42/1.16 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 0.42/1.16 ) }.
% 0.42/1.16 { ! distinct_lines( X, X ) }.
% 0.42/1.16 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.42/1.16 }.
% 0.42/1.16 { ! unequally_directed_lines( X, X ) }.
% 0.42/1.16 { ! unequally_directed_lines( X, Y ), unequally_directed_lines( X, Z ),
% 0.42/1.16 unequally_directed_lines( Y, Z ) }.
% 0.42/1.16 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.42/1.16 reverse_line( Y ) ), alpha9( X, Z ), unequally_directed_lines( Y, Z ) }.
% 0.42/1.16 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.42/1.16 reverse_line( Y ) ), alpha9( X, Z ), unequally_directed_lines( Y,
% 0.42/1.16 reverse_line( Z ) ) }.
% 0.42/1.16 { ! alpha9( X, Y ), unequally_directed_lines( X, Y ) }.
% 0.42/1.16 { ! alpha9( X, Y ), unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.42/1.16 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.42/1.16 reverse_line( Y ) ), alpha9( X, Y ) }.
% 0.42/1.16 { ! line( X ), ! line( Y ), unequally_directed_lines( X, Y ),
% 0.42/1.16 unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.42/1.16 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.42/1.16 reverse_line( Y ) ), left_convergent_lines( X, Y ), left_convergent_lines
% 0.42/1.16 ( X, reverse_line( Y ) ) }.
% 0.42/1.17 { ! left_apart_point( X, Y ) }.
% 0.42/1.17 { ! left_apart_point( X, reverse_line( Y ) ) }.
% 0.42/1.17 { ! left_convergent_lines( X, Y ) }.
% 0.42/1.17 { ! left_convergent_lines( X, reverse_line( Y ) ) }.
% 0.42/1.17 { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line(
% 0.42/1.17 line_connecting( X, Y ) ) }.
% 0.42/1.17 { ! line( X ), ! line( Y ), ! unequally_directed_lines( X, Y ), !
% 0.42/1.17 unequally_directed_lines( X, reverse_line( Y ) ), point(
% 0.42/1.17 intersection_point( X, Y ) ) }.
% 0.42/1.17 { ! point( Y ), ! line( X ), line( parallel_through_point( X, Y ) ) }.
% 0.42/1.17 { ! line( X ), line( reverse_line( X ) ) }.
% 0.42/1.17 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 0.42/1.17 , Y ) ) }.
% 0.42/1.17 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 0.42/1.17 , Y ) ) }.
% 0.42/1.17 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.42/1.17 reverse_line( Y ) ), ! apart_point_and_line( intersection_point( X, Y ),
% 0.42/1.17 X ) }.
% 0.42/1.17 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.42/1.17 reverse_line( Y ) ), ! apart_point_and_line( intersection_point( X, Y ),
% 0.42/1.17 Y ) }.
% 0.42/1.17 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 0.42/1.17 { ! distinct_lines( X, reverse_line( X ) ) }.
% 0.42/1.17 { ! unequally_directed_lines( line_connecting( X, Y ), reverse_line(
% 0.42/1.17 line_connecting( Y, X ) ) ) }.
% 0.42/1.17 { ! unequally_directed_lines( parallel_through_point( Y, X ), Y ) }.
% 0.42/1.17 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), left_apart_point( X
% 0.42/1.17 , Z ), left_apart_point( Y, Z ), left_apart_point( X, T ),
% 0.42/1.17 left_apart_point( Y, T ), left_apart_point( X, reverse_line( Z ) ),
% 0.42/1.17 left_apart_point( Y, reverse_line( Z ) ), left_apart_point( X,
% 0.42/1.17 reverse_line( T ) ), left_apart_point( Y, reverse_line( T ) ) }.
% 0.42/1.17 { ! distinct_points( X, Y ), ! left_apart_point( X, Z ), left_apart_point(
% 0.42/1.17 Y, Z ), left_convergent_lines( line_connecting( X, Y ), Z ) }.
% 0.42/1.17 { ! left_apart_point( X, Y ), distinct_points( X, Z ), left_apart_point( Z
% 0.42/1.17 , Y ) }.
% 0.42/1.17 { ! left_apart_point( X, Y ), ! unequally_directed_lines( Y, Z ),
% 0.42/1.17 distinct_lines( Y, Z ), left_apart_point( X, reverse_line( Z ) ) }.
% 0.42/1.17 { ! left_convergent_lines( X, Y ), unequally_directed_lines( Y, Z ),
% 0.42/1.17 left_convergent_lines( X, Z ) }.
% 0.42/1.17 { unequally_directed_lines( reverse_line( reverse_line( skol1 ) ), skol1 )
% 0.42/1.17 }.
% 0.42/1.17
% 0.42/1.17 percentage equality = 0.000000, percentage horn = 0.794118
% 0.42/1.17 This a non-horn, non-equality problem
% 0.42/1.17
% 0.42/1.17
% 0.42/1.17 Options Used:
% 0.42/1.17
% 0.42/1.17 useres = 1
% 0.42/1.17 useparamod = 0
% 0.42/1.17 useeqrefl = 0
% 0.42/1.17 useeqfact = 0
% 0.42/1.17 usefactor = 1
% 0.42/1.17 usesimpsplitting = 0
% 0.42/1.17 usesimpdemod = 0
% 0.42/1.17 usesimpres = 3
% 0.42/1.17
% 0.42/1.17 resimpinuse = 1000
% 0.42/1.17 resimpclauses = 20000
% 0.42/1.17 substype = standard
% 0.42/1.17 backwardsubs = 1
% 0.42/1.17 selectoldest = 5
% 0.42/1.17
% 0.42/1.17 litorderings [0] = split
% 0.42/1.17 litorderings [1] = liftord
% 0.42/1.17
% 0.42/1.17 termordering = none
% 0.42/1.17
% 0.42/1.17 litapriori = 1
% 0.42/1.17 termapriori = 0
% 0.42/1.17 litaposteriori = 0
% 0.42/1.17 termaposteriori = 0
% 0.42/1.17 demodaposteriori = 0
% 0.42/1.17 ordereqreflfact = 0
% 0.42/1.17
% 0.42/1.17 litselect = none
% 0.42/1.17
% 0.42/1.17 maxweight = 15
% 0.42/1.17 maxdepth = 30000
% 0.42/1.17 maxlength = 115
% 0.42/1.17 maxnrvars = 195
% 0.42/1.17 excuselevel = 1
% 0.42/1.17 increasemaxweight = 1
% 0.42/1.17
% 0.42/1.17 maxselected = 10000000
% 0.42/1.17 maxnrclauses = 10000000
% 0.42/1.17
% 0.42/1.17 showgenerated = 0
% 0.42/1.17 showkept = 0
% 0.42/1.17 showselected = 0
% 0.42/1.17 showdeleted = 0
% 0.42/1.17 showresimp = 1
% 0.42/1.17 showstatus = 2000
% 0.42/1.17
% 0.42/1.17 prologoutput = 0
% 0.42/1.17 nrgoals = 5000000
% 0.42/1.17 totalproof = 1
% 0.42/1.17
% 0.42/1.17 Symbols occurring in the translation:
% 0.42/1.17
% 0.42/1.17 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.42/1.17 . [1, 2] (w:1, o:21, a:1, s:1, b:0),
% 0.42/1.17 ! [4, 1] (w:0, o:13, a:1, s:1, b:0),
% 0.42/1.17 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.42/1.17 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.42/1.17 apart_point_and_line [37, 2] (w:1, o:45, a:1, s:1, b:0),
% 0.42/1.17 left_apart_point [38, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.42/1.17 reverse_line [39, 1] (w:1, o:18, a:1, s:1, b:0),
% 0.42/1.17 convergent_lines [41, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.42/1.17 unequally_directed_lines [42, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.42/1.17 divides_points [44, 3] (w:1, o:58, a:1, s:1, b:0),
% 0.42/1.17 before_on_line [45, 3] (w:1, o:63, a:1, s:1, b:0),
% 0.42/1.17 distinct_points [46, 2] (w:1, o:49, a:1, s:1, b:0),
% 0.42/1.17 line_connecting [47, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.42/1.17 between_on_line [49, 4] (w:1, o:66, a:1, s:1, b:0),
% 0.42/1.17 distinct_lines [50, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.42/1.17 line [52, 1] (w:1, o:19, a:1, s:1, b:0),
% 0.42/1.17 left_convergent_lines [53, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.42/1.17 point [54, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.42/1.17 intersection_point [55, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.42/1.17 parallel_through_point [56, 2] (w:1, o:54, a:1, s:1, b:0),
% 0.42/1.17 alpha1 [57, 3] (w:1, o:59, a:1, s:1, b:0),
% 0.42/1.17 alpha2 [58, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.42/1.17 alpha3 [59, 4] (w:1, o:64, a:1, s:1, b:0),
% 0.42/1.17 alpha4 [60, 3] (w:1, o:60, a:1, s:1, b:0),
% 0.42/1.17 alpha5 [61, 2] (w:1, o:56, a:1, s:1, b:0),
% 0.42/1.17 alpha6 [62, 4] (w:1, o:65, a:1, s:1, b:0),
% 0.42/1.17 alpha7 [63, 3] (w:1, o:61, a:1, s:1, b:0),
% 0.42/1.17 alpha8 [64, 3] (w:1, o:62, a:1, s:1, b:0),
% 0.42/1.17 alpha9 [65, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.42/1.17 skol1 [66, 0] (w:1, o:12, a:1, s:1, b:0).
% 0.42/1.17
% 0.42/1.17
% 0.42/1.17 Starting Search:
% 0.42/1.17
% 0.42/1.17 *** allocated 15000 integers for clauses
% 0.42/1.17 *** allocated 22500 integers for clauses
% 0.42/1.17 *** allocated 33750 integers for clauses
% 0.42/1.17
% 0.42/1.17 Bliksems!, er is een bewijs:
% 0.42/1.17 % SZS status Theorem
% 0.42/1.17 % SZS output start Refutation
% 0.42/1.17
% 0.42/1.17 (43) {G0,W3,D2,L1,V1,M1} I { ! unequally_directed_lines( X, X ) }.
% 0.42/1.17 (44) {G0,W9,D2,L3,V3,M3} I { unequally_directed_lines( X, Z ),
% 0.42/1.17 unequally_directed_lines( Y, Z ), ! unequally_directed_lines( X, Y ) }.
% 0.42/1.17 (51) {G0,W14,D3,L4,V2,M2} I { ! unequally_directed_lines( X, Y ), !
% 0.42/1.17 unequally_directed_lines( X, reverse_line( Y ) ), left_convergent_lines(
% 0.42/1.17 X, reverse_line( Y ) ), left_convergent_lines( X, Y ) }.
% 0.42/1.17 (53) {G0,W3,D2,L1,V2,M1} I { ! left_convergent_lines( X, Y ) }.
% 0.42/1.17 (65) {G0,W5,D3,L1,V2,M1} I { ! unequally_directed_lines(
% 0.42/1.17 parallel_through_point( Y, X ), Y ) }.
% 0.42/1.17 (67) {G0,W5,D4,L1,V0,M1} I { unequally_directed_lines( reverse_line(
% 0.42/1.17 reverse_line( skol1 ) ), skol1 ) }.
% 0.42/1.17 (109) {G1,W6,D2,L2,V2,M2} R(44,43) { ! unequally_directed_lines( Y, X ),
% 0.42/1.17 unequally_directed_lines( X, Y ) }.
% 0.42/1.17 (120) {G2,W5,D4,L1,V0,M1} R(109,67) { unequally_directed_lines( skol1,
% 0.42/1.17 reverse_line( reverse_line( skol1 ) ) ) }.
% 0.42/1.17 (121) {G2,W5,D3,L1,V2,M1} R(109,65) { ! unequally_directed_lines( X,
% 0.42/1.17 parallel_through_point( X, Y ) ) }.
% 0.42/1.17 (122) {G3,W8,D3,L2,V3,M2} R(121,44) { ! unequally_directed_lines( Y, X ),
% 0.42/1.17 unequally_directed_lines( X, parallel_through_point( Y, Z ) ) }.
% 0.42/1.17 (147) {G4,W7,D5,L1,V1,M1} R(122,67) { unequally_directed_lines( skol1,
% 0.42/1.17 parallel_through_point( reverse_line( reverse_line( skol1 ) ), X ) ) }.
% 0.42/1.17 (428) {G1,W7,D3,L2,V2,M2} S(51);r(53);r(53) { ! unequally_directed_lines( X
% 0.42/1.17 , reverse_line( Y ) ), ! unequally_directed_lines( X, Y ) }.
% 0.42/1.17 (462) {G3,W4,D3,L1,V0,M1} R(428,120) { ! unequally_directed_lines( skol1,
% 0.42/1.17 reverse_line( skol1 ) ) }.
% 0.42/1.17 (465) {G2,W7,D3,L2,V2,M2} R(428,109) { ! unequally_directed_lines( Y, X ),
% 0.42/1.17 ! unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.42/1.17 (479) {G4,W3,D2,L1,V1,M1} R(462,44);r(465) { ! unequally_directed_lines(
% 0.42/1.17 skol1, X ) }.
% 0.42/1.17 (486) {G5,W0,D0,L0,V0,M0} R(479,147) { }.
% 0.42/1.17
% 0.42/1.17
% 0.42/1.17 % SZS output end Refutation
% 0.42/1.17 found a proof!
% 0.42/1.17
% 0.42/1.17
% 0.42/1.17 Unprocessed initial clauses:
% 0.42/1.17
% 0.42/1.17 (488) {G0,W10,D3,L3,V2,M3} { ! apart_point_and_line( X, Y ),
% 0.42/1.17 left_apart_point( X, Y ), left_apart_point( X, reverse_line( Y ) ) }.
% 0.42/1.17 (489) {G0,W6,D2,L2,V2,M2} { ! left_apart_point( X, Y ),
% 0.42/1.17 apart_point_and_line( X, Y ) }.
% 0.42/1.17 (490) {G0,W7,D3,L2,V2,M2} { ! left_apart_point( X, reverse_line( Y ) ),
% 0.42/1.17 apart_point_and_line( X, Y ) }.
% 0.42/1.17 (491) {G0,W6,D2,L2,V2,M2} { ! convergent_lines( X, Y ),
% 0.42/1.17 unequally_directed_lines( X, Y ) }.
% 0.42/1.17 (492) {G0,W7,D3,L2,V2,M2} { ! convergent_lines( X, Y ),
% 0.42/1.17 unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.42/1.17 (493) {G0,W10,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y ), !
% 0.42/1.17 unequally_directed_lines( X, reverse_line( Y ) ), convergent_lines( X, Y
% 0.42/1.17 ) }.
% 0.42/1.17 (494) {G0,W12,D2,L3,V3,M3} { ! divides_points( Z, X, Y ), alpha1( X, Y, Z
% 0.42/1.17 ), alpha4( X, Y, Z ) }.
% 0.42/1.17 (495) {G0,W8,D2,L2,V3,M2} { ! alpha1( X, Y, Z ), divides_points( Z, X, Y )
% 0.42/1.17 }.
% 0.42/1.17 (496) {G0,W8,D2,L2,V3,M2} { ! alpha4( X, Y, Z ), divides_points( Z, X, Y )
% 0.42/1.17 }.
% 0.42/1.17 (497) {G0,W8,D3,L2,V3,M2} { ! alpha4( X, Y, Z ), left_apart_point( X,
% 0.42/1.17 reverse_line( Z ) ) }.
% 0.42/1.17 (498) {G0,W7,D2,L2,V3,M2} { ! alpha4( X, Y, Z ), left_apart_point( Y, Z )
% 0.42/1.17 }.
% 0.42/1.17 (499) {G0,W11,D3,L3,V3,M3} { ! left_apart_point( X, reverse_line( Z ) ), !
% 0.42/1.17 left_apart_point( Y, Z ), alpha4( X, Y, Z ) }.
% 0.42/1.17 (500) {G0,W7,D2,L2,V3,M2} { ! alpha1( X, Y, Z ), left_apart_point( X, Z )
% 0.42/1.17 }.
% 0.42/1.17 (501) {G0,W8,D3,L2,V3,M2} { ! alpha1( X, Y, Z ), left_apart_point( Y,
% 0.42/1.17 reverse_line( Z ) ) }.
% 0.42/1.17 (502) {G0,W11,D3,L3,V3,M3} { ! left_apart_point( X, Z ), !
% 0.42/1.17 left_apart_point( Y, reverse_line( Z ) ), alpha1( X, Y, Z ) }.
% 0.42/1.17 (503) {G0,W7,D2,L2,V3,M2} { ! before_on_line( X, Y, Z ), distinct_points(
% 0.42/1.17 Y, Z ) }.
% 0.42/1.17 (504) {G0,W8,D2,L2,V3,M2} { ! before_on_line( X, Y, Z ), alpha7( X, Y, Z )
% 0.42/1.17 }.
% 0.42/1.17 (505) {G0,W11,D2,L3,V3,M3} { ! distinct_points( Y, Z ), ! alpha7( X, Y, Z
% 0.42/1.17 ), before_on_line( X, Y, Z ) }.
% 0.42/1.17 (506) {G0,W7,D2,L2,V3,M2} { ! alpha7( X, Y, Z ), alpha2( X, Y ) }.
% 0.42/1.17 (507) {G0,W8,D2,L2,V3,M2} { ! alpha7( X, Y, Z ), alpha8( X, Y, Z ) }.
% 0.42/1.17 (508) {G0,W11,D2,L3,V3,M3} { ! alpha2( X, Y ), ! alpha8( X, Y, Z ), alpha7
% 0.42/1.17 ( X, Y, Z ) }.
% 0.42/1.17 (509) {G0,W7,D2,L2,V3,M2} { ! alpha8( X, Y, Z ), alpha5( X, Z ) }.
% 0.42/1.17 (510) {G0,W9,D3,L2,V3,M2} { ! alpha8( X, Y, Z ), !
% 0.42/1.17 unequally_directed_lines( X, line_connecting( Y, Z ) ) }.
% 0.42/1.17 (511) {G0,W12,D3,L3,V3,M3} { ! alpha5( X, Z ), unequally_directed_lines( X
% 0.42/1.17 , line_connecting( Y, Z ) ), alpha8( X, Y, Z ) }.
% 0.42/1.17 (512) {G0,W6,D2,L2,V2,M2} { ! alpha5( X, Y ), ! left_apart_point( Y, X )
% 0.42/1.17 }.
% 0.42/1.17 (513) {G0,W7,D3,L2,V2,M2} { ! alpha5( X, Y ), ! left_apart_point( Y,
% 0.42/1.17 reverse_line( X ) ) }.
% 0.42/1.17 (514) {G0,W10,D3,L3,V2,M3} { left_apart_point( Y, X ), left_apart_point( Y
% 0.42/1.17 , reverse_line( X ) ), alpha5( X, Y ) }.
% 0.42/1.17 (515) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), ! left_apart_point( Y, X )
% 0.42/1.17 }.
% 0.42/1.17 (516) {G0,W7,D3,L2,V2,M2} { ! alpha2( X, Y ), ! left_apart_point( Y,
% 0.42/1.17 reverse_line( X ) ) }.
% 0.42/1.17 (517) {G0,W10,D3,L3,V2,M3} { left_apart_point( Y, X ), left_apart_point( Y
% 0.42/1.17 , reverse_line( X ) ), alpha2( X, Y ) }.
% 0.42/1.17 (518) {G0,W15,D2,L3,V4,M3} { ! between_on_line( X, Y, Z, T ), alpha3( X, Y
% 0.42/1.17 , Z, T ), alpha6( X, Y, Z, T ) }.
% 0.42/1.17 (519) {G0,W10,D2,L2,V4,M2} { ! alpha3( X, Y, Z, T ), between_on_line( X, Y
% 0.42/1.17 , Z, T ) }.
% 0.42/1.17 (520) {G0,W10,D2,L2,V4,M2} { ! alpha6( X, Y, Z, T ), between_on_line( X, Y
% 0.42/1.17 , Z, T ) }.
% 0.42/1.17 (521) {G0,W9,D2,L2,V4,M2} { ! alpha6( X, Y, Z, T ), before_on_line( X, T,
% 0.42/1.17 Z ) }.
% 0.42/1.17 (522) {G0,W9,D2,L2,V4,M2} { ! alpha6( X, Y, Z, T ), before_on_line( X, Z,
% 0.42/1.17 Y ) }.
% 0.42/1.17 (523) {G0,W13,D2,L3,V4,M3} { ! before_on_line( X, T, Z ), ! before_on_line
% 0.42/1.17 ( X, Z, Y ), alpha6( X, Y, Z, T ) }.
% 0.42/1.17 (524) {G0,W9,D2,L2,V4,M2} { ! alpha3( X, Y, Z, T ), before_on_line( X, Y,
% 0.42/1.17 Z ) }.
% 0.42/1.17 (525) {G0,W9,D2,L2,V4,M2} { ! alpha3( X, Y, Z, T ), before_on_line( X, Z,
% 0.42/1.17 T ) }.
% 0.42/1.17 (526) {G0,W13,D2,L3,V4,M3} { ! before_on_line( X, Y, Z ), ! before_on_line
% 0.42/1.17 ( X, Z, T ), alpha3( X, Y, Z, T ) }.
% 0.42/1.17 (527) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 0.42/1.17 (528) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 0.42/1.17 , Z ), distinct_points( Y, Z ) }.
% 0.42/1.17 (529) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.42/1.17 (530) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X, Z
% 0.42/1.17 ), distinct_lines( Y, Z ) }.
% 0.42/1.17 (531) {G0,W3,D2,L1,V1,M1} { ! unequally_directed_lines( X, X ) }.
% 0.42/1.17 (532) {G0,W9,D2,L3,V3,M3} { ! unequally_directed_lines( X, Y ),
% 0.42/1.17 unequally_directed_lines( X, Z ), unequally_directed_lines( Y, Z ) }.
% 0.42/1.17 (533) {G0,W13,D3,L4,V3,M4} { ! unequally_directed_lines( X, Y ), !
% 0.42/1.17 unequally_directed_lines( X, reverse_line( Y ) ), alpha9( X, Z ),
% 0.42/1.17 unequally_directed_lines( Y, Z ) }.
% 0.42/1.17 (534) {G0,W14,D3,L4,V3,M4} { ! unequally_directed_lines( X, Y ), !
% 0.42/1.17 unequally_directed_lines( X, reverse_line( Y ) ), alpha9( X, Z ),
% 0.42/1.17 unequally_directed_lines( Y, reverse_line( Z ) ) }.
% 0.42/1.17 (535) {G0,W6,D2,L2,V2,M2} { ! alpha9( X, Y ), unequally_directed_lines( X
% 0.42/1.17 , Y ) }.
% 0.42/1.17 (536) {G0,W7,D3,L2,V2,M2} { ! alpha9( X, Y ), unequally_directed_lines( X
% 0.42/1.17 , reverse_line( Y ) ) }.
% 0.42/1.17 (537) {G0,W10,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y ), !
% 0.42/1.17 unequally_directed_lines( X, reverse_line( Y ) ), alpha9( X, Y ) }.
% 0.42/1.17 (538) {G0,W11,D3,L4,V2,M4} { ! line( X ), ! line( Y ),
% 0.42/1.17 unequally_directed_lines( X, Y ), unequally_directed_lines( X,
% 0.42/1.17 reverse_line( Y ) ) }.
% 0.42/1.17 (539) {G0,W14,D3,L4,V2,M4} { ! unequally_directed_lines( X, Y ), !
% 0.42/1.17 unequally_directed_lines( X, reverse_line( Y ) ), left_convergent_lines(
% 0.42/1.17 X, Y ), left_convergent_lines( X, reverse_line( Y ) ) }.
% 0.42/1.17 (540) {G0,W3,D2,L1,V2,M1} { ! left_apart_point( X, Y ) }.
% 0.42/1.17 (541) {G0,W4,D3,L1,V2,M1} { ! left_apart_point( X, reverse_line( Y ) ) }.
% 0.42/1.17 (542) {G0,W3,D2,L1,V2,M1} { ! left_convergent_lines( X, Y ) }.
% 0.42/1.17 (543) {G0,W4,D3,L1,V2,M1} { ! left_convergent_lines( X, reverse_line( Y )
% 0.42/1.17 ) }.
% 0.42/1.17 (544) {G0,W11,D3,L4,V2,M4} { ! point( X ), ! point( Y ), ! distinct_points
% 0.42/1.17 ( X, Y ), line( line_connecting( X, Y ) ) }.
% 0.42/1.17 (545) {G0,W15,D3,L5,V2,M5} { ! line( X ), ! line( Y ), !
% 0.42/1.17 unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.42/1.17 reverse_line( Y ) ), point( intersection_point( X, Y ) ) }.
% 0.42/1.17 (546) {G0,W8,D3,L3,V2,M3} { ! point( Y ), ! line( X ), line(
% 0.42/1.17 parallel_through_point( X, Y ) ) }.
% 0.42/1.17 (547) {G0,W5,D3,L2,V1,M2} { ! line( X ), line( reverse_line( X ) ) }.
% 0.42/1.17 (548) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.42/1.17 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 0.42/1.17 (549) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.42/1.17 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 0.42/1.17 (550) {G0,W12,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y ), !
% 0.42/1.17 unequally_directed_lines( X, reverse_line( Y ) ), ! apart_point_and_line
% 0.42/1.17 ( intersection_point( X, Y ), X ) }.
% 0.42/1.17 (551) {G0,W12,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y ), !
% 0.42/1.17 unequally_directed_lines( X, reverse_line( Y ) ), ! apart_point_and_line
% 0.42/1.17 ( intersection_point( X, Y ), Y ) }.
% 0.42/1.17 (552) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.42/1.17 parallel_through_point( Y, X ) ) }.
% 0.42/1.17 (553) {G0,W4,D3,L1,V1,M1} { ! distinct_lines( X, reverse_line( X ) ) }.
% 0.42/1.17 (554) {G0,W8,D4,L1,V2,M1} { ! unequally_directed_lines( line_connecting( X
% 0.42/1.17 , Y ), reverse_line( line_connecting( Y, X ) ) ) }.
% 0.42/1.17 (555) {G0,W5,D3,L1,V2,M1} { ! unequally_directed_lines(
% 0.42/1.17 parallel_through_point( Y, X ), Y ) }.
% 0.42/1.17 (556) {G0,W34,D3,L10,V4,M10} { ! distinct_points( X, Y ), ! distinct_lines
% 0.42/1.17 ( Z, T ), left_apart_point( X, Z ), left_apart_point( Y, Z ),
% 0.42/1.17 left_apart_point( X, T ), left_apart_point( Y, T ), left_apart_point( X,
% 0.42/1.17 reverse_line( Z ) ), left_apart_point( Y, reverse_line( Z ) ),
% 0.42/1.17 left_apart_point( X, reverse_line( T ) ), left_apart_point( Y,
% 0.42/1.17 reverse_line( T ) ) }.
% 0.42/1.17 (557) {G0,W14,D3,L4,V3,M4} { ! distinct_points( X, Y ), ! left_apart_point
% 0.42/1.17 ( X, Z ), left_apart_point( Y, Z ), left_convergent_lines(
% 0.42/1.17 line_connecting( X, Y ), Z ) }.
% 0.42/1.17 (558) {G0,W9,D2,L3,V3,M3} { ! left_apart_point( X, Y ), distinct_points( X
% 0.42/1.17 , Z ), left_apart_point( Z, Y ) }.
% 0.42/1.17 (559) {G0,W13,D3,L4,V3,M4} { ! left_apart_point( X, Y ), !
% 0.42/1.17 unequally_directed_lines( Y, Z ), distinct_lines( Y, Z ),
% 0.42/1.17 left_apart_point( X, reverse_line( Z ) ) }.
% 0.42/1.17 (560) {G0,W9,D2,L3,V3,M3} { ! left_convergent_lines( X, Y ),
% 0.42/1.17 unequally_directed_lines( Y, Z ), left_convergent_lines( X, Z ) }.
% 0.42/1.17 (561) {G0,W5,D4,L1,V0,M1} { unequally_directed_lines( reverse_line(
% 0.42/1.17 reverse_line( skol1 ) ), skol1 ) }.
% 0.42/1.17
% 0.42/1.17
% 0.42/1.17 Total Proof:
% 0.42/1.17
% 0.42/1.17 subsumption: (43) {G0,W3,D2,L1,V1,M1} I { ! unequally_directed_lines( X, X
% 0.42/1.17 ) }.
% 0.42/1.17 parent0: (531) {G0,W3,D2,L1,V1,M1} { ! unequally_directed_lines( X, X )
% 0.42/1.17 }.
% 0.42/1.17 substitution0:
% 0.42/1.17 X := X
% 0.42/1.17 end
% 0.42/1.17 permutation0:
% 0.42/1.17 0 ==> 0
% 0.42/1.17 end
% 0.42/1.17
% 0.42/1.17 subsumption: (44) {G0,W9,D2,L3,V3,M3} I { unequally_directed_lines( X, Z )
% 0.42/1.17 , unequally_directed_lines( Y, Z ), ! unequally_directed_lines( X, Y )
% 0.42/1.17 }.
% 0.42/1.17 parent0: (532) {G0,W9,D2,L3,V3,M3} { ! unequally_directed_lines( X, Y ),
% 0.42/1.17 unequally_directed_lines( X, Z ), unequally_directed_lines( Y, Z ) }.
% 0.42/1.17 substitution0:
% 0.42/1.17 X := X
% 0.42/1.17 Y := Y
% 0.42/1.17 Z := Z
% 0.42/1.17 end
% 0.42/1.17 permutation0:
% 0.42/1.17 0 ==> 2
% 0.42/1.17 1 ==> 0
% 0.42/1.17 2 ==> 1
% 0.42/1.17 end
% 0.42/1.17
% 0.42/1.17 subsumption: (51) {G0,W14,D3,L4,V2,M2} I { ! unequally_directed_lines( X, Y
% 0.42/1.17 ), ! unequally_directed_lines( X, reverse_line( Y ) ),
% 0.42/1.17 left_convergent_lines( X, reverse_line( Y ) ), left_convergent_lines( X,
% 0.42/1.17 Y ) }.
% 0.42/1.17 parent0: (539) {G0,W14,D3,L4,V2,M4} { ! unequally_directed_lines( X, Y ),
% 0.42/1.17 ! unequally_directed_lines( X, reverse_line( Y ) ), left_convergent_lines
% 0.42/1.17 ( X, Y ), left_convergent_lines( X, reverse_line( Y ) ) }.
% 0.42/1.17 substitution0:
% 0.42/1.17 X := X
% 0.42/1.17 Y := Y
% 0.42/1.17 end
% 0.42/1.17 permutation0:
% 0.42/1.17 0 ==> 0
% 0.42/1.17 1 ==> 1
% 0.42/1.17 2 ==> 3
% 0.42/1.17 3 ==> 2
% 0.42/1.17 end
% 0.42/1.17
% 0.42/1.17 subsumption: (53) {G0,W3,D2,L1,V2,M1} I { ! left_convergent_lines( X, Y )
% 0.42/1.17 }.
% 0.42/1.17 parent0: (542) {G0,W3,D2,L1,V2,M1} { ! left_convergent_lines( X, Y ) }.
% 0.42/1.17 substitution0:
% 0.42/1.17 X := X
% 0.42/1.17 Y := Y
% 0.42/1.17 end
% 0.42/1.17 permutation0:
% 0.42/1.17 0 ==> 0
% 0.42/1.17 end
% 0.42/1.17
% 0.42/1.17 subsumption: (65) {G0,W5,D3,L1,V2,M1} I { ! unequally_directed_lines(
% 0.42/1.17 parallel_through_point( Y, X ), Y ) }.
% 0.42/1.17 parent0: (555) {G0,W5,D3,L1,V2,M1} { ! unequally_directed_lines(
% 0.42/1.17 parallel_through_point( Y, X ), Y ) }.
% 0.42/1.17 substitution0:
% 0.42/1.17 X := X
% 0.42/1.17 Y := Y
% 0.42/1.17 end
% 0.42/1.17 permutation0:
% 0.42/1.17 0 ==> 0
% 0.42/1.17 end
% 0.42/1.17
% 0.42/1.17 subsumption: (67) {G0,W5,D4,L1,V0,M1} I { unequally_directed_lines(
% 0.42/1.17 reverse_line( reverse_line( skol1 ) ), skol1 ) }.
% 0.42/1.17 parent0: (561) {G0,W5,D4,L1,V0,M1} { unequally_directed_lines(
% 0.42/1.17 reverse_line( reverse_line( skol1 ) ), skol1 ) }.
% 0.42/1.17 substitution0:
% 0.42/1.17 end
% 0.42/1.17 permutation0:
% 0.42/1.17 0 ==> 0
% 0.42/1.17 end
% 0.42/1.17
% 0.42/1.17 resolution: (625) {G1,W6,D2,L2,V2,M2} { unequally_directed_lines( Y, X ),
% 0.42/1.17 ! unequally_directed_lines( X, Y ) }.
% 0.42/1.17 parent0[0]: (43) {G0,W3,D2,L1,V1,M1} I { ! unequally_directed_lines( X, X )
% 0.42/1.17 }.
% 0.42/1.17 parent1[0]: (44) {G0,W9,D2,L3,V3,M3} I { unequally_directed_lines( X, Z ),
% 0.42/1.17 unequally_directed_lines( Y, Z ), ! unequally_directed_lines( X, Y ) }.
% 0.42/1.17 substitution0:
% 0.42/1.17 X := X
% 0.42/1.17 end
% 0.42/1.17 substitution1:
% 0.42/1.17 X := X
% 0.42/1.17 Y := Y
% 0.42/1.17 Z := X
% 0.42/1.17 end
% 0.42/1.17
% 0.42/1.17 subsumption: (109) {G1,W6,D2,L2,V2,M2} R(44,43) { !
% 0.42/1.17 unequally_directed_lines( Y, X ), unequally_directed_lines( X, Y ) }.
% 0.42/1.17 parent0: (625) {G1,W6,D2,L2,V2,M2} { unequally_directed_lines( Y, X ), !
% 0.42/1.17 unequally_directed_lines( X, Y ) }.
% 0.42/1.17 substitution0:
% 0.42/1.17 X := Y
% 0.42/1.17 Y := X
% 0.42/1.17 end
% 0.42/1.17 permutation0:
% 0.42/1.17 0 ==> 1
% 0.42/1.17 1 ==> 0
% 0.42/1.17 end
% 0.42/1.17
% 0.42/1.17 resolution: (627) {G1,W5,D4,L1,V0,M1} { unequally_directed_lines( skol1,
% 0.42/1.17 reverse_line( reverse_line( skol1 ) ) ) }.
% 0.42/1.17 parent0[0]: (109) {G1,W6,D2,L2,V2,M2} R(44,43) { ! unequally_directed_lines
% 0.42/1.17 ( Y, X ), unequally_directed_lines( X, Y ) }.
% 0.42/1.17 parent1[0]: (67) {G0,W5,D4,L1,V0,M1} I { unequally_directed_lines(
% 0.42/1.17 reverse_line( reverse_line( skol1 ) ), skol1 ) }.
% 0.42/1.17 substitution0:
% 0.42/1.17 X := skol1
% 0.42/1.17 Y := reverse_line( reverse_line( skol1 ) )
% 0.42/1.17 end
% 0.42/1.17 substitution1:
% 0.42/1.17 end
% 0.42/1.17
% 0.42/1.17 subsumption: (120) {G2,W5,D4,L1,V0,M1} R(109,67) { unequally_directed_lines
% 0.42/1.17 ( skol1, reverse_line( reverse_line( skol1 ) ) ) }.
% 0.42/1.17 parent0: (627) {G1,W5,D4,L1,V0,M1} { unequally_directed_lines( skol1,
% 0.42/1.17 reverse_line( reverse_line( skol1 ) ) ) }.
% 0.42/1.17 substitution0:
% 0.42/1.17 end
% 0.42/1.17 permutation0:
% 0.42/1.17 0 ==> 0
% 0.42/1.17 end
% 0.42/1.17
% 0.42/1.17 resolution: (628) {G1,W5,D3,L1,V2,M1} { ! unequally_directed_lines( X,
% 0.42/1.17 parallel_through_point( X, Y ) ) }.
% 0.42/1.17 parent0[0]: (65) {G0,W5,D3,L1,V2,M1} I { ! unequally_directed_lines(
% 0.42/1.17 parallel_through_point( Y, X ), Y ) }.
% 0.42/1.17 parent1[1]: (109) {G1,W6,D2,L2,V2,M2} R(44,43) { ! unequally_directed_lines
% 0.42/1.17 ( Y, X ), unequally_directed_lines( X, Y ) }.
% 0.42/1.17 substitution0:
% 0.42/1.17 X := Y
% 0.42/1.17 Y := X
% 0.42/1.17 end
% 0.42/1.17 substitution1:
% 0.42/1.17 X := parallel_through_point( X, Y )
% 0.42/1.17 Y := X
% 0.42/1.17 end
% 0.42/1.17
% 0.42/1.17 subsumption: (121) {G2,W5,D3,L1,V2,M1} R(109,65) { !
% 0.42/1.17 unequally_directed_lines( X, parallel_through_point( X, Y ) ) }.
% 0.42/1.17 parent0: (628) {G1,W5,D3,L1,V2,M1} { ! unequally_directed_lines( X,
% 0.42/1.17 parallel_through_point( X, Y ) ) }.
% 0.42/1.17 substitution0:
% 0.42/1.17 X := X
% 0.42/1.17 Y := Y
% 0.42/1.17 end
% 0.42/1.17 permutation0:
% 0.42/1.17 0 ==> 0
% 0.42/1.17 end
% 0.42/1.17
% 0.42/1.17 resolution: (629) {G1,W8,D3,L2,V3,M2} { unequally_directed_lines( Z,
% 0.42/1.17 parallel_through_point( X, Y ) ), ! unequally_directed_lines( X, Z ) }.
% 0.42/1.17 parent0[0]: (121) {G2,W5,D3,L1,V2,M1} R(109,65) { !
% 0.42/1.17 unequally_directed_lines( X, parallel_through_point( X, Y ) ) }.
% 0.42/1.17 parent1[0]: (44) {G0,W9,D2,L3,V3,M3} I { unequally_directed_lines( X, Z ),
% 0.42/1.17 unequally_directed_lines( Y, Z ), ! unequally_directed_lines( X, Y ) }.
% 0.42/1.17 substitution0:
% 0.42/1.17 X := X
% 0.42/1.17 Y := Y
% 0.42/1.17 end
% 0.42/1.17 substitution1:
% 0.42/1.17 X := X
% 0.42/1.17 Y := Z
% 0.42/1.17 Z := parallel_through_point( X, Y )
% 0.42/1.17 end
% 0.42/1.17
% 0.42/1.17 subsumption: (122) {G3,W8,D3,L2,V3,M2} R(121,44) { !
% 0.42/1.17 unequally_directed_lines( Y, X ), unequally_directed_lines( X,
% 0.42/1.17 parallel_through_point( Y, Z ) ) }.
% 0.42/1.17 parent0: (629) {G1,W8,D3,L2,V3,M2} { unequally_directed_lines( Z,
% 0.42/1.17 parallel_through_point( X, Y ) ), ! unequally_directed_lines( X, Z ) }.
% 0.42/1.17 substitution0:
% 0.42/1.17 X := Y
% 0.42/1.17 Y := Z
% 0.42/1.17 Z := X
% 0.42/1.17 end
% 0.42/1.17 permutation0:
% 0.42/1.17 0 ==> 1
% 0.42/1.17 1 ==> 0
% 0.42/1.17 end
% 0.42/1.17
% 0.42/1.17 resolution: (631) {G1,W7,D5,L1,V1,M1} { unequally_directed_lines( skol1,
% 0.42/1.17 parallel_through_point( reverse_line( reverse_line( skol1 ) ), X ) ) }.
% 0.42/1.17 parent0[0]: (122) {G3,W8,D3,L2,V3,M2} R(121,44) { !
% 0.42/1.17 unequally_directed_lines( Y, X ), unequally_directed_lines( X,
% 0.42/1.17 parallel_through_point( Y, Z ) ) }.
% 0.42/1.17 parent1[0]: (67) {G0,W5,D4,L1,V0,M1} I { unequally_directed_lines(
% 0.42/1.17 reverse_line( reverse_line( skol1 ) ), skol1 ) }.
% 0.42/1.17 substitution0:
% 0.42/1.17 X := skol1
% 0.42/1.17 Y := reverse_line( reverse_line( skol1 ) )
% 0.42/1.17 Z := X
% 0.42/1.17 end
% 0.42/1.17 substitution1:
% 0.42/1.17 end
% 0.42/1.17
% 0.42/1.17 subsumption: (147) {G4,W7,D5,L1,V1,M1} R(122,67) { unequally_directed_lines
% 0.42/1.17 ( skol1, parallel_through_point( reverse_line( reverse_line( skol1 ) ), X
% 0.42/1.17 ) ) }.
% 0.42/1.17 parent0: (631) {G1,W7,D5,L1,V1,M1} { unequally_directed_lines( skol1,
% 0.42/1.17 parallel_through_point( reverse_line( reverse_line( skol1 ) ), X ) ) }.
% 0.42/1.17 substitution0:
% 0.42/1.17 X := X
% 0.42/1.17 end
% 0.42/1.17 permutation0:
% 0.42/1.17 0 ==> 0
% 0.42/1.17 end
% 0.42/1.17
% 0.42/1.17 resolution: (632) {G1,W10,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y
% 0.42/1.17 ), ! unequally_directed_lines( X, reverse_line( Y ) ),
% 0.42/1.17 left_convergent_lines( X, Y ) }.
% 0.42/1.17 parent0[0]: (53) {G0,W3,D2,L1,V2,M1} I { ! left_convergent_lines( X, Y )
% 0.42/1.17 }.
% 0.42/1.17 parent1[2]: (51) {G0,W14,D3,L4,V2,M2} I { ! unequally_directed_lines( X, Y
% 0.42/1.17 ), ! unequally_directed_lines( X, reverse_line( Y ) ),
% 0.42/1.17 left_convergent_lines( X, reverse_line( Y ) ), left_convergent_lines( X,
% 0.42/1.17 Y ) }.
% 0.42/1.17 substitution0:
% 0.42/1.17 X := X
% 0.42/1.17 Y := reverse_line( Y )
% 0.42/1.17 end
% 0.42/1.17 substitution1:
% 0.42/1.17 X := X
% 0.42/1.17 Y := Y
% 0.42/1.17 end
% 0.42/1.17
% 0.42/1.17 resolution: (634) {G1,W7,D3,L2,V2,M2} { ! unequally_directed_lines( X, Y )
% 0.42/1.17 , ! unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.42/1.17 parent0[0]: (53) {G0,W3,D2,L1,V2,M1} I { ! left_convergent_lines( X, Y )
% 0.42/1.17 }.
% 0.42/1.17 parent1[2]: (632) {G1,W10,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y
% 0.42/1.17 ), ! unequally_directed_lines( X, reverse_line( Y ) ),
% 0.42/1.17 left_convergent_lines( X, Y ) }.
% 0.42/1.17 substitution0:
% 0.42/1.17 X := X
% 0.42/1.17 Y := Y
% 0.42/1.17 end
% 0.42/1.17 substitution1:
% 0.42/1.17 X := X
% 0.42/1.17 Y := Y
% 0.42/1.17 end
% 0.42/1.17
% 0.42/1.17 subsumption: (428) {G1,W7,D3,L2,V2,M2} S(51);r(53);r(53) { !
% 0.42/1.17 unequally_directed_lines( X, reverse_line( Y ) ), !
% 0.42/1.17 unequally_directed_lines( X, Y ) }.
% 0.42/1.17 parent0: (634) {G1,W7,D3,L2,V2,M2} { ! unequally_directed_lines( X, Y ), !
% 0.42/1.17 unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.42/1.17 substitution0:
% 0.42/1.17 X := X
% 0.42/1.17 Y := Y
% 0.42/1.17 end
% 0.42/1.17 permutation0:
% 0.42/1.17 0 ==> 1
% 0.42/1.17 1 ==> 0
% 0.42/1.17 end
% 0.42/1.17
% 0.42/1.17 resolution: (635) {G2,W4,D3,L1,V0,M1} { ! unequally_directed_lines( skol1
% 0.42/1.17 , reverse_line( skol1 ) ) }.
% 0.42/1.17 parent0[0]: (428) {G1,W7,D3,L2,V2,M2} S(51);r(53);r(53) { !
% 0.42/1.17 unequally_directed_lines( X, reverse_line( Y ) ), !
% 0.42/1.17 unequally_directed_lines( X, Y ) }.
% 0.42/1.17 parent1[0]: (120) {G2,W5,D4,L1,V0,M1} R(109,67) { unequally_directed_lines
% 0.42/1.17 ( skol1, reverse_line( reverse_line( skol1 ) ) ) }.
% 0.42/1.17 substitution0:
% 0.42/1.17 X := skol1
% 0.42/1.17 Y := reverse_line( skol1 )
% 0.42/1.17 end
% 0.42/1.17 substitution1:
% 0.42/1.17 end
% 0.42/1.17
% 0.42/1.17 subsumption: (462) {G3,W4,D3,L1,V0,M1} R(428,120) { !
% 0.42/1.17 unequally_directed_lines( skol1, reverse_line( skol1 ) ) }.
% 0.42/1.17 parent0: (635) {G2,W4,D3,L1,V0,M1} { ! unequally_directed_lines( skol1,
% 0.42/1.17 reverse_line( skol1 ) ) }.
% 0.42/1.17 substitution0:
% 0.42/1.17 end
% 0.42/1.17 permutation0:
% 0.42/1.17 0 ==> 0
% 0.42/1.17 end
% 0.42/1.17
% 0.42/1.17 resolution: (638) {G2,W7,D3,L2,V2,M2} { ! unequally_directed_lines( X,
% 0.42/1.17 reverse_line( Y ) ), ! unequally_directed_lines( Y, X ) }.
% 0.42/1.17 parent0[1]: (428) {G1,W7,D3,L2,V2,M2} S(51);r(53);r(53) { !
% 0.42/1.17 unequally_directed_lines( X, reverse_line( Y ) ), !
% 0.42/1.17 unequally_directed_lines( X, Y ) }.
% 0.42/1.17 parent1[1]: (109) {G1,W6,D2,L2,V2,M2} R(44,43) { ! unequally_directed_lines
% 0.42/1.17 ( Y, X ), unequally_directed_lines( X, Y ) }.
% 0.42/1.17 substitution0:
% 0.42/1.17 X := X
% 0.42/1.17 Y := Y
% 0.42/1.17 end
% 0.42/1.17 substitution1:
% 0.42/1.17 X := X
% 0.42/1.17 Y := Y
% 0.42/1.17 end
% 0.42/1.17
% 0.42/1.17 subsumption: (465) {G2,W7,D3,L2,V2,M2} R(428,109) { !
% 0.42/1.17 unequally_directed_lines( Y, X ), ! unequally_directed_lines( X,
% 0.42/1.17 reverse_line( Y ) ) }.
% 0.42/1.17 parent0: (638) {G2,W7,D3,L2,V2,M2} { ! unequally_directed_lines( X,
% 0.42/1.17 reverse_line( Y ) ), ! unequally_directed_lines( Y, X ) }.
% 0.42/1.17 substitution0:
% 0.42/1.17 X := X
% 0.42/1.17 Y := Y
% 0.42/1.17 end
% 0.42/1.17 permutation0:
% 0.42/1.17 0 ==> 1
% 0.42/1.17 1 ==> 0
% 0.42/1.17 end
% 0.42/1.17
% 0.42/1.17 resolution: (639) {G1,W7,D3,L2,V1,M2} { unequally_directed_lines( X,
% 0.42/1.17 reverse_line( skol1 ) ), ! unequally_directed_lines( skol1, X ) }.
% 0.42/1.17 parent0[0]: (462) {G3,W4,D3,L1,V0,M1} R(428,120) { !
% 0.42/1.17 unequally_directed_lines( skol1, reverse_line( skol1 ) ) }.
% 0.42/1.17 parent1[0]: (44) {G0,W9,D2,L3,V3,M3} I { unequally_directed_lines( X, Z ),
% 0.42/1.17 unequally_directed_lines( Y, Z ), ! unequally_directed_lines( X, Y ) }.
% 0.42/1.17 substitution0:
% 0.42/1.17 end
% 0.42/1.17 substitution1:
% 0.42/1.17 X := skol1
% 0.42/1.17 Y := X
% 0.42/1.17 Z := reverse_line( skol1 )
% 0.42/1.17 end
% 0.42/1.17
% 0.42/1.17 resolution: (642) {G2,W6,D2,L2,V1,M2} { ! unequally_directed_lines( skol1
% 0.42/1.17 , X ), ! unequally_directed_lines( skol1, X ) }.
% 0.42/1.17 parent0[1]: (465) {G2,W7,D3,L2,V2,M2} R(428,109) { !
% 0.42/1.17 unequally_directed_lines( Y, X ), ! unequally_directed_lines( X,
% 0.42/1.17 reverse_line( Y ) ) }.
% 0.42/1.17 parent1[0]: (639) {G1,W7,D3,L2,V1,M2} { unequally_directed_lines( X,
% 0.42/1.17 reverse_line( skol1 ) ), ! unequally_directed_lines( skol1, X ) }.
% 0.42/1.17 substitution0:
% 0.42/1.17 X := X
% 0.42/1.17 Y := skol1
% 0.42/1.17 end
% 0.42/1.17 substitution1:
% 0.42/1.17 X := X
% 0.42/1.17 end
% 0.42/1.17
% 0.42/1.17 factor: (643) {G2,W3,D2,L1,V1,M1} { ! unequally_directed_lines( skol1, X )
% 0.42/1.17 }.
% 0.42/1.17 parent0[0, 1]: (642) {G2,W6,D2,L2,V1,M2} { ! unequally_directed_lines(
% 0.42/1.17 skol1, X ), ! unequally_directed_lines( skol1, X ) }.
% 0.42/1.17 substitution0:
% 0.42/1.17 X := X
% 0.42/1.17 end
% 0.42/1.17
% 0.42/1.17 subsumption: (479) {G4,W3,D2,L1,V1,M1} R(462,44);r(465) { !
% 0.42/1.17 unequally_directed_lines( skol1, X ) }.
% 0.42/1.17 parent0: (643) {G2,W3,D2,L1,V1,M1} { ! unequally_directed_lines( skol1, X
% 0.42/1.17 ) }.
% 0.42/1.17 substitution0:
% 0.42/1.17 X := X
% 0.42/1.17 end
% 0.42/1.17 permutation0:
% 0.42/1.17 0 ==> 0
% 0.42/1.17 end
% 0.42/1.17
% 0.42/1.17 resolution: (644) {G5,W0,D0,L0,V0,M0} { }.
% 0.42/1.17 parent0[0]: (479) {G4,W3,D2,L1,V1,M1} R(462,44);r(465) { !
% 0.42/1.17 unequally_directed_lines( skol1, X ) }.
% 0.42/1.17 parent1[0]: (147) {G4,W7,D5,L1,V1,M1} R(122,67) { unequally_directed_lines
% 0.42/1.17 ( skol1, parallel_through_point( reverse_line( reverse_line( skol1 ) ), X
% 0.42/1.17 ) ) }.
% 0.42/1.17 substitution0:
% 0.42/1.17 X := parallel_through_point( reverse_line( reverse_line( skol1 ) ), X )
% 0.42/1.17 end
% 0.42/1.17 substitution1:
% 0.42/1.17 X := X
% 0.42/1.17 end
% 0.42/1.17
% 0.42/1.17 subsumption: (486) {G5,W0,D0,L0,V0,M0} R(479,147) { }.
% 0.42/1.17 parent0: (644) {G5,W0,D0,L0,V0,M0} { }.
% 0.42/1.17 substitution0:
% 0.42/1.17 end
% 0.42/1.17 permutation0:
% 0.42/1.17 end
% 0.42/1.17
% 0.42/1.17 Proof check complete!
% 0.42/1.17
% 0.42/1.17 Memory use:
% 0.42/1.17
% 0.42/1.17 space for terms: 6852
% 0.42/1.17 space for clauses: 24830
% 0.42/1.17
% 0.42/1.17
% 0.42/1.17 clauses generated: 1316
% 0.42/1.17 clauses kept: 487
% 0.42/1.17 clauses selected: 129
% 0.42/1.17 clauses deleted: 23
% 0.42/1.17 clauses inuse deleted: 0
% 0.42/1.17
% 0.42/1.17 subsentry: 6491
% 0.42/1.17 literals s-matched: 3515
% 0.42/1.17 literals matched: 3465
% 0.42/1.17 full subsumption: 812
% 0.42/1.17
% 0.42/1.17 checksum: 1650666541
% 0.42/1.17
% 0.42/1.17
% 0.42/1.17 Bliksem ended
%------------------------------------------------------------------------------