TSTP Solution File: GEO228+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO228+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n028.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 02:53:03 EDT 2022
% Result : Theorem 0.43s 1.16s
% Output : Refutation 0.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO228+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.07/0.13 % Command : bliksem %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Sat Jun 18 08:42:59 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.43/1.16 *** allocated 10000 integers for termspace/termends
% 0.43/1.16 *** allocated 10000 integers for clauses
% 0.43/1.16 *** allocated 10000 integers for justifications
% 0.43/1.16 Bliksem 1.12
% 0.43/1.16
% 0.43/1.16
% 0.43/1.16 Automatic Strategy Selection
% 0.43/1.16
% 0.43/1.16
% 0.43/1.16 Clauses:
% 0.43/1.16
% 0.43/1.16 { ! apart_point_and_line( X, Y ), left_apart_point( X, Y ),
% 0.43/1.16 left_apart_point( X, reverse_line( Y ) ) }.
% 0.43/1.16 { ! left_apart_point( X, Y ), apart_point_and_line( X, Y ) }.
% 0.43/1.16 { ! left_apart_point( X, reverse_line( Y ) ), apart_point_and_line( X, Y )
% 0.43/1.16 }.
% 0.43/1.16 { ! convergent_lines( X, Y ), unequally_directed_lines( X, Y ) }.
% 0.43/1.16 { ! convergent_lines( X, Y ), unequally_directed_lines( X, reverse_line( Y
% 0.43/1.16 ) ) }.
% 0.43/1.16 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.43/1.16 reverse_line( Y ) ), convergent_lines( X, Y ) }.
% 0.43/1.16 { ! divides_points( Z, X, Y ), alpha1( X, Y, Z ), alpha4( X, Y, Z ) }.
% 0.43/1.16 { ! alpha1( X, Y, Z ), divides_points( Z, X, Y ) }.
% 0.43/1.16 { ! alpha4( X, Y, Z ), divides_points( Z, X, Y ) }.
% 0.43/1.16 { ! alpha4( X, Y, Z ), left_apart_point( X, reverse_line( Z ) ) }.
% 0.43/1.16 { ! alpha4( X, Y, Z ), left_apart_point( Y, Z ) }.
% 0.43/1.16 { ! left_apart_point( X, reverse_line( Z ) ), ! left_apart_point( Y, Z ),
% 0.43/1.16 alpha4( X, Y, Z ) }.
% 0.43/1.16 { ! alpha1( X, Y, Z ), left_apart_point( X, Z ) }.
% 0.43/1.16 { ! alpha1( X, Y, Z ), left_apart_point( Y, reverse_line( Z ) ) }.
% 0.43/1.16 { ! left_apart_point( X, Z ), ! left_apart_point( Y, reverse_line( Z ) ),
% 0.43/1.16 alpha1( X, Y, Z ) }.
% 0.43/1.16 { ! before_on_line( X, Y, Z ), distinct_points( Y, Z ) }.
% 0.43/1.16 { ! before_on_line( X, Y, Z ), alpha7( X, Y, Z ) }.
% 0.43/1.16 { ! distinct_points( Y, Z ), ! alpha7( X, Y, Z ), before_on_line( X, Y, Z )
% 0.43/1.16 }.
% 0.43/1.16 { ! alpha7( X, Y, Z ), alpha2( X, Y ) }.
% 0.43/1.16 { ! alpha7( X, Y, Z ), alpha8( X, Y, Z ) }.
% 0.43/1.16 { ! alpha2( X, Y ), ! alpha8( X, Y, Z ), alpha7( X, Y, Z ) }.
% 0.43/1.16 { ! alpha8( X, Y, Z ), alpha5( X, Z ) }.
% 0.43/1.16 { ! alpha8( X, Y, Z ), ! unequally_directed_lines( X, line_connecting( Y, Z
% 0.43/1.16 ) ) }.
% 0.43/1.16 { ! alpha5( X, Z ), unequally_directed_lines( X, line_connecting( Y, Z ) )
% 0.43/1.16 , alpha8( X, Y, Z ) }.
% 0.43/1.16 { ! alpha5( X, Y ), ! left_apart_point( Y, X ) }.
% 0.43/1.16 { ! alpha5( X, Y ), ! left_apart_point( Y, reverse_line( X ) ) }.
% 0.43/1.16 { left_apart_point( Y, X ), left_apart_point( Y, reverse_line( X ) ),
% 0.43/1.16 alpha5( X, Y ) }.
% 0.43/1.16 { ! alpha2( X, Y ), ! left_apart_point( Y, X ) }.
% 0.43/1.16 { ! alpha2( X, Y ), ! left_apart_point( Y, reverse_line( X ) ) }.
% 0.43/1.16 { left_apart_point( Y, X ), left_apart_point( Y, reverse_line( X ) ),
% 0.43/1.16 alpha2( X, Y ) }.
% 0.43/1.16 { ! between_on_line( X, Y, Z, T ), alpha3( X, Y, Z, T ), alpha6( X, Y, Z, T
% 0.43/1.16 ) }.
% 0.43/1.16 { ! alpha3( X, Y, Z, T ), between_on_line( X, Y, Z, T ) }.
% 0.43/1.16 { ! alpha6( X, Y, Z, T ), between_on_line( X, Y, Z, T ) }.
% 0.43/1.16 { ! alpha6( X, Y, Z, T ), before_on_line( X, T, Z ) }.
% 0.43/1.16 { ! alpha6( X, Y, Z, T ), before_on_line( X, Z, Y ) }.
% 0.43/1.16 { ! before_on_line( X, T, Z ), ! before_on_line( X, Z, Y ), alpha6( X, Y, Z
% 0.43/1.16 , T ) }.
% 0.43/1.16 { ! alpha3( X, Y, Z, T ), before_on_line( X, Y, Z ) }.
% 0.43/1.16 { ! alpha3( X, Y, Z, T ), before_on_line( X, Z, T ) }.
% 0.43/1.16 { ! before_on_line( X, Y, Z ), ! before_on_line( X, Z, T ), alpha3( X, Y, Z
% 0.43/1.16 , T ) }.
% 0.43/1.16 { ! distinct_points( X, X ) }.
% 0.43/1.16 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 0.43/1.16 ) }.
% 0.43/1.16 { ! distinct_lines( X, X ) }.
% 0.43/1.16 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.43/1.16 }.
% 0.43/1.16 { ! unequally_directed_lines( X, X ) }.
% 0.43/1.16 { ! unequally_directed_lines( X, Y ), unequally_directed_lines( X, Z ),
% 0.43/1.16 unequally_directed_lines( Y, Z ) }.
% 0.43/1.16 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.43/1.16 reverse_line( Y ) ), alpha9( X, Z ), unequally_directed_lines( Y, Z ) }.
% 0.43/1.16 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.43/1.16 reverse_line( Y ) ), alpha9( X, Z ), unequally_directed_lines( Y,
% 0.43/1.16 reverse_line( Z ) ) }.
% 0.43/1.16 { ! alpha9( X, Y ), unequally_directed_lines( X, Y ) }.
% 0.43/1.16 { ! alpha9( X, Y ), unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.43/1.16 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.43/1.16 reverse_line( Y ) ), alpha9( X, Y ) }.
% 0.43/1.16 { ! line( X ), ! line( Y ), unequally_directed_lines( X, Y ),
% 0.43/1.16 unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.43/1.16 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.43/1.16 reverse_line( Y ) ), left_convergent_lines( X, Y ), left_convergent_lines
% 0.43/1.16 ( X, reverse_line( Y ) ) }.
% 0.43/1.16 { ! left_apart_point( X, Y ) }.
% 0.43/1.16 { ! left_apart_point( X, reverse_line( Y ) ) }.
% 0.43/1.16 { ! left_convergent_lines( X, Y ) }.
% 0.43/1.16 { ! left_convergent_lines( X, reverse_line( Y ) ) }.
% 0.43/1.16 { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line(
% 0.43/1.16 line_connecting( X, Y ) ) }.
% 0.43/1.16 { ! line( X ), ! line( Y ), ! unequally_directed_lines( X, Y ), !
% 0.43/1.16 unequally_directed_lines( X, reverse_line( Y ) ), point(
% 0.43/1.16 intersection_point( X, Y ) ) }.
% 0.43/1.16 { ! point( Y ), ! line( X ), line( parallel_through_point( X, Y ) ) }.
% 0.43/1.16 { ! line( X ), line( reverse_line( X ) ) }.
% 0.43/1.16 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 0.43/1.16 , Y ) ) }.
% 0.43/1.16 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 0.43/1.16 , Y ) ) }.
% 0.43/1.16 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.43/1.16 reverse_line( Y ) ), ! apart_point_and_line( intersection_point( X, Y ),
% 0.43/1.16 X ) }.
% 0.43/1.16 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.43/1.16 reverse_line( Y ) ), ! apart_point_and_line( intersection_point( X, Y ),
% 0.43/1.16 Y ) }.
% 0.43/1.16 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 0.43/1.16 { ! distinct_lines( X, reverse_line( X ) ) }.
% 0.43/1.16 { ! unequally_directed_lines( line_connecting( X, Y ), reverse_line(
% 0.43/1.16 line_connecting( Y, X ) ) ) }.
% 0.43/1.16 { ! unequally_directed_lines( parallel_through_point( Y, X ), Y ) }.
% 0.43/1.16 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), left_apart_point( X
% 0.43/1.16 , Z ), left_apart_point( Y, Z ), left_apart_point( X, T ),
% 0.43/1.16 left_apart_point( Y, T ), left_apart_point( X, reverse_line( Z ) ),
% 0.43/1.16 left_apart_point( Y, reverse_line( Z ) ), left_apart_point( X,
% 0.43/1.16 reverse_line( T ) ), left_apart_point( Y, reverse_line( T ) ) }.
% 0.43/1.16 { ! distinct_points( X, Y ), ! left_apart_point( X, Z ), left_apart_point(
% 0.43/1.16 Y, Z ), left_convergent_lines( line_connecting( X, Y ), Z ) }.
% 0.43/1.16 { ! left_apart_point( X, Y ), distinct_points( X, Z ), left_apart_point( Z
% 0.43/1.16 , Y ) }.
% 0.43/1.16 { ! left_apart_point( X, Y ), ! unequally_directed_lines( Y, Z ),
% 0.43/1.16 distinct_lines( Y, Z ), left_apart_point( X, reverse_line( Z ) ) }.
% 0.43/1.16 { ! left_convergent_lines( X, Y ), unequally_directed_lines( Y, Z ),
% 0.43/1.16 left_convergent_lines( X, Z ) }.
% 0.43/1.16 { alpha10( skol1, skol2 ), ! unequally_directed_lines( skol1, skol2 ), !
% 0.43/1.16 unequally_directed_lines( skol1, reverse_line( skol2 ) ) }.
% 0.43/1.16 { alpha10( skol1, skol2 ), convergent_lines( skol1, skol2 ) }.
% 0.43/1.16 { ! alpha10( X, Y ), ! convergent_lines( X, Y ) }.
% 0.43/1.16 { ! alpha10( X, Y ), unequally_directed_lines( X, Y ) }.
% 0.43/1.16 { ! alpha10( X, Y ), unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.43/1.16 { convergent_lines( X, Y ), ! unequally_directed_lines( X, Y ), !
% 0.43/1.16 unequally_directed_lines( X, reverse_line( Y ) ), alpha10( X, Y ) }.
% 0.43/1.16
% 0.43/1.16 percentage equality = 0.000000, percentage horn = 0.791667
% 0.43/1.16 This a non-horn, non-equality problem
% 0.43/1.16
% 0.43/1.16
% 0.43/1.16 Options Used:
% 0.43/1.16
% 0.43/1.16 useres = 1
% 0.43/1.16 useparamod = 0
% 0.43/1.16 useeqrefl = 0
% 0.43/1.16 useeqfact = 0
% 0.43/1.16 usefactor = 1
% 0.43/1.16 usesimpsplitting = 0
% 0.43/1.16 usesimpdemod = 0
% 0.43/1.16 usesimpres = 3
% 0.43/1.16
% 0.43/1.16 resimpinuse = 1000
% 0.43/1.16 resimpclauses = 20000
% 0.43/1.16 substype = standard
% 0.43/1.16 backwardsubs = 1
% 0.43/1.16 selectoldest = 5
% 0.43/1.16
% 0.43/1.16 litorderings [0] = split
% 0.43/1.16 litorderings [1] = liftord
% 0.43/1.16
% 0.43/1.16 termordering = none
% 0.43/1.16
% 0.43/1.16 litapriori = 1
% 0.43/1.16 termapriori = 0
% 0.43/1.16 litaposteriori = 0
% 0.43/1.16 termaposteriori = 0
% 0.43/1.16 demodaposteriori = 0
% 0.43/1.16 ordereqreflfact = 0
% 0.43/1.16
% 0.43/1.16 litselect = none
% 0.43/1.16
% 0.43/1.16 maxweight = 15
% 0.43/1.16 maxdepth = 30000
% 0.43/1.16 maxlength = 115
% 0.43/1.16 maxnrvars = 195
% 0.43/1.16 excuselevel = 1
% 0.43/1.16 increasemaxweight = 1
% 0.43/1.16
% 0.43/1.16 maxselected = 10000000
% 0.43/1.16 maxnrclauses = 10000000
% 0.43/1.16
% 0.43/1.16 showgenerated = 0
% 0.43/1.16 showkept = 0
% 0.43/1.16 showselected = 0
% 0.43/1.16 showdeleted = 0
% 0.43/1.16 showresimp = 1
% 0.43/1.16 showstatus = 2000
% 0.43/1.16
% 0.43/1.16 prologoutput = 0
% 0.43/1.16 nrgoals = 5000000
% 0.43/1.16 totalproof = 1
% 0.43/1.16
% 0.43/1.16 Symbols occurring in the translation:
% 0.43/1.16
% 0.43/1.16 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.43/1.16 . [1, 2] (w:1, o:22, a:1, s:1, b:0),
% 0.43/1.16 ! [4, 1] (w:0, o:14, a:1, s:1, b:0),
% 0.43/1.16 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.43/1.16 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.43/1.16 apart_point_and_line [37, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.43/1.16 left_apart_point [38, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.43/1.16 reverse_line [39, 1] (w:1, o:19, a:1, s:1, b:0),
% 0.43/1.16 convergent_lines [41, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.43/1.16 unequally_directed_lines [42, 2] (w:1, o:49, a:1, s:1, b:0),
% 0.43/1.16 divides_points [44, 3] (w:1, o:60, a:1, s:1, b:0),
% 0.43/1.16 before_on_line [45, 3] (w:1, o:65, a:1, s:1, b:0),
% 0.43/1.16 distinct_points [46, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.43/1.16 line_connecting [47, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.43/1.16 between_on_line [49, 4] (w:1, o:68, a:1, s:1, b:0),
% 0.43/1.16 distinct_lines [50, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.43/1.16 line [52, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.43/1.16 left_convergent_lines [53, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.43/1.16 point [54, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.43/1.16 intersection_point [55, 2] (w:1, o:54, a:1, s:1, b:0),
% 0.43/1.16 parallel_through_point [56, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.43/1.16 alpha1 [57, 3] (w:1, o:61, a:1, s:1, b:0),
% 0.43/1.16 alpha2 [58, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.43/1.16 alpha3 [59, 4] (w:1, o:66, a:1, s:1, b:0),
% 0.43/1.16 alpha4 [60, 3] (w:1, o:62, a:1, s:1, b:0),
% 0.43/1.16 alpha5 [61, 2] (w:1, o:58, a:1, s:1, b:0),
% 0.43/1.16 alpha6 [62, 4] (w:1, o:67, a:1, s:1, b:0),
% 0.43/1.16 alpha7 [63, 3] (w:1, o:63, a:1, s:1, b:0),
% 0.43/1.16 alpha8 [64, 3] (w:1, o:64, a:1, s:1, b:0),
% 0.43/1.16 alpha9 [65, 2] (w:1, o:59, a:1, s:1, b:0),
% 0.43/1.16 alpha10 [66, 2] (w:1, o:56, a:1, s:1, b:0),
% 0.43/1.16 skol1 [67, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.43/1.16 skol2 [68, 0] (w:1, o:13, a:1, s:1, b:0).
% 0.43/1.16
% 0.43/1.16
% 0.43/1.16 Starting Search:
% 0.43/1.16
% 0.43/1.16 *** allocated 15000 integers for clauses
% 0.43/1.16 *** allocated 22500 integers for clauses
% 0.43/1.16
% 0.43/1.16 Bliksems!, er is een bewijs:
% 0.43/1.16 % SZS status Theorem
% 0.43/1.16 % SZS output start Refutation
% 0.43/1.16
% 0.43/1.16 (3) {G0,W6,D2,L2,V2,M1} I { ! convergent_lines( X, Y ),
% 0.43/1.16 unequally_directed_lines( X, Y ) }.
% 0.43/1.16 (4) {G0,W7,D3,L2,V2,M1} I { ! convergent_lines( X, Y ),
% 0.43/1.16 unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.43/1.16 (5) {G0,W10,D3,L3,V2,M2} I { convergent_lines( X, Y ), !
% 0.43/1.16 unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.43/1.16 reverse_line( Y ) ) }.
% 0.43/1.16 (43) {G0,W3,D2,L1,V1,M1} I { ! unequally_directed_lines( X, X ) }.
% 0.43/1.16 (44) {G0,W9,D2,L3,V3,M3} I { unequally_directed_lines( X, Z ),
% 0.43/1.16 unequally_directed_lines( Y, Z ), ! unequally_directed_lines( X, Y ) }.
% 0.43/1.16 (51) {G0,W14,D3,L4,V2,M2} I { ! unequally_directed_lines( X, Y ), !
% 0.43/1.16 unequally_directed_lines( X, reverse_line( Y ) ), left_convergent_lines(
% 0.43/1.16 X, reverse_line( Y ) ), left_convergent_lines( X, Y ) }.
% 0.43/1.16 (53) {G0,W3,D2,L1,V2,M1} I { ! left_convergent_lines( X, Y ) }.
% 0.43/1.16 (65) {G0,W5,D3,L1,V2,M1} I { ! unequally_directed_lines(
% 0.43/1.16 parallel_through_point( Y, X ), Y ) }.
% 0.43/1.16 (68) {G0,W6,D2,L2,V0,M1} I { convergent_lines( skol1, skol2 ), alpha10(
% 0.43/1.16 skol1, skol2 ) }.
% 0.43/1.16 (70) {G0,W6,D2,L2,V2,M1} I { unequally_directed_lines( X, Y ), ! alpha10( X
% 0.43/1.16 , Y ) }.
% 0.43/1.16 (71) {G0,W7,D3,L2,V2,M1} I { unequally_directed_lines( X, reverse_line( Y )
% 0.43/1.16 ), ! alpha10( X, Y ) }.
% 0.43/1.16 (81) {G1,W3,D2,L1,V0,M1} R(68,70);r(3) { unequally_directed_lines( skol1,
% 0.43/1.16 skol2 ) }.
% 0.43/1.16 (82) {G2,W7,D3,L2,V0,M1} R(5,81) { convergent_lines( skol1, skol2 ), !
% 0.43/1.16 unequally_directed_lines( skol1, reverse_line( skol2 ) ) }.
% 0.43/1.16 (91) {G3,W3,D2,L1,V0,M1} R(71,68);r(82) { convergent_lines( skol1, skol2 )
% 0.43/1.16 }.
% 0.43/1.16 (115) {G1,W6,D2,L2,V2,M2} R(44,43) { ! unequally_directed_lines( Y, X ),
% 0.43/1.16 unequally_directed_lines( X, Y ) }.
% 0.43/1.16 (127) {G2,W5,D3,L1,V2,M1} R(115,65) { ! unequally_directed_lines( X,
% 0.43/1.16 parallel_through_point( X, Y ) ) }.
% 0.43/1.16 (129) {G3,W8,D3,L2,V3,M2} R(127,44) { ! unequally_directed_lines( Y, X ),
% 0.43/1.16 unequally_directed_lines( X, parallel_through_point( Y, Z ) ) }.
% 0.43/1.16 (194) {G4,W8,D3,L2,V3,M2} R(129,115) { unequally_directed_lines(
% 0.43/1.16 parallel_through_point( X, Z ), Y ), ! unequally_directed_lines( X, Y )
% 0.43/1.16 }.
% 0.43/1.16 (262) {G5,W9,D3,L2,V3,M1} R(194,4) { ! convergent_lines( X, Z ),
% 0.43/1.16 unequally_directed_lines( parallel_through_point( X, Y ), reverse_line( Z
% 0.43/1.16 ) ) }.
% 0.43/1.16 (263) {G5,W8,D3,L2,V3,M1} R(194,3) { ! convergent_lines( X, Z ),
% 0.43/1.16 unequally_directed_lines( parallel_through_point( X, Y ), Z ) }.
% 0.43/1.16 (354) {G6,W8,D3,L2,V3,M2} R(263,5);r(262) { convergent_lines(
% 0.43/1.16 parallel_through_point( X, Z ), Y ), ! convergent_lines( X, Y ) }.
% 0.43/1.16 (357) {G7,W5,D3,L1,V1,M1} R(354,91) { convergent_lines(
% 0.43/1.16 parallel_through_point( skol1, X ), skol2 ) }.
% 0.43/1.16 (358) {G8,W7,D4,L1,V2,M1} R(357,354) { convergent_lines(
% 0.43/1.16 parallel_through_point( parallel_through_point( skol1, X ), Y ), skol2 )
% 0.43/1.16 }.
% 0.43/1.16 (360) {G1,W7,D3,L2,V2,M2} S(51);r(53);r(53) { ! unequally_directed_lines( X
% 0.43/1.16 , reverse_line( Y ) ), ! unequally_directed_lines( X, Y ) }.
% 0.43/1.16 (362) {G6,W3,D2,L1,V2,M1} R(360,263);r(262) { ! convergent_lines( X, Z )
% 0.43/1.16 }.
% 0.43/1.16 (402) {G9,W0,D0,L0,V0,M0} R(362,358) { }.
% 0.43/1.16
% 0.43/1.16
% 0.43/1.16 % SZS output end Refutation
% 0.43/1.16 found a proof!
% 0.43/1.16
% 0.43/1.16 *** allocated 33750 integers for clauses
% 0.43/1.16
% 0.43/1.16 Unprocessed initial clauses:
% 0.43/1.16
% 0.43/1.16 (404) {G0,W10,D3,L3,V2,M3} { ! apart_point_and_line( X, Y ),
% 0.43/1.16 left_apart_point( X, Y ), left_apart_point( X, reverse_line( Y ) ) }.
% 0.43/1.16 (405) {G0,W6,D2,L2,V2,M2} { ! left_apart_point( X, Y ),
% 0.43/1.16 apart_point_and_line( X, Y ) }.
% 0.43/1.16 (406) {G0,W7,D3,L2,V2,M2} { ! left_apart_point( X, reverse_line( Y ) ),
% 0.43/1.16 apart_point_and_line( X, Y ) }.
% 0.43/1.16 (407) {G0,W6,D2,L2,V2,M2} { ! convergent_lines( X, Y ),
% 0.43/1.16 unequally_directed_lines( X, Y ) }.
% 0.43/1.16 (408) {G0,W7,D3,L2,V2,M2} { ! convergent_lines( X, Y ),
% 0.43/1.16 unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.43/1.16 (409) {G0,W10,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y ), !
% 0.43/1.16 unequally_directed_lines( X, reverse_line( Y ) ), convergent_lines( X, Y
% 0.43/1.16 ) }.
% 0.43/1.16 (410) {G0,W12,D2,L3,V3,M3} { ! divides_points( Z, X, Y ), alpha1( X, Y, Z
% 0.43/1.16 ), alpha4( X, Y, Z ) }.
% 0.43/1.16 (411) {G0,W8,D2,L2,V3,M2} { ! alpha1( X, Y, Z ), divides_points( Z, X, Y )
% 0.43/1.16 }.
% 0.43/1.16 (412) {G0,W8,D2,L2,V3,M2} { ! alpha4( X, Y, Z ), divides_points( Z, X, Y )
% 0.43/1.16 }.
% 0.43/1.16 (413) {G0,W8,D3,L2,V3,M2} { ! alpha4( X, Y, Z ), left_apart_point( X,
% 0.43/1.16 reverse_line( Z ) ) }.
% 0.43/1.16 (414) {G0,W7,D2,L2,V3,M2} { ! alpha4( X, Y, Z ), left_apart_point( Y, Z )
% 0.43/1.16 }.
% 0.43/1.16 (415) {G0,W11,D3,L3,V3,M3} { ! left_apart_point( X, reverse_line( Z ) ), !
% 0.43/1.16 left_apart_point( Y, Z ), alpha4( X, Y, Z ) }.
% 0.43/1.16 (416) {G0,W7,D2,L2,V3,M2} { ! alpha1( X, Y, Z ), left_apart_point( X, Z )
% 0.43/1.16 }.
% 0.43/1.16 (417) {G0,W8,D3,L2,V3,M2} { ! alpha1( X, Y, Z ), left_apart_point( Y,
% 0.43/1.16 reverse_line( Z ) ) }.
% 0.43/1.16 (418) {G0,W11,D3,L3,V3,M3} { ! left_apart_point( X, Z ), !
% 0.43/1.16 left_apart_point( Y, reverse_line( Z ) ), alpha1( X, Y, Z ) }.
% 0.43/1.16 (419) {G0,W7,D2,L2,V3,M2} { ! before_on_line( X, Y, Z ), distinct_points(
% 0.43/1.16 Y, Z ) }.
% 0.43/1.16 (420) {G0,W8,D2,L2,V3,M2} { ! before_on_line( X, Y, Z ), alpha7( X, Y, Z )
% 0.43/1.16 }.
% 0.43/1.16 (421) {G0,W11,D2,L3,V3,M3} { ! distinct_points( Y, Z ), ! alpha7( X, Y, Z
% 0.43/1.16 ), before_on_line( X, Y, Z ) }.
% 0.43/1.16 (422) {G0,W7,D2,L2,V3,M2} { ! alpha7( X, Y, Z ), alpha2( X, Y ) }.
% 0.43/1.16 (423) {G0,W8,D2,L2,V3,M2} { ! alpha7( X, Y, Z ), alpha8( X, Y, Z ) }.
% 0.43/1.16 (424) {G0,W11,D2,L3,V3,M3} { ! alpha2( X, Y ), ! alpha8( X, Y, Z ), alpha7
% 0.43/1.16 ( X, Y, Z ) }.
% 0.43/1.16 (425) {G0,W7,D2,L2,V3,M2} { ! alpha8( X, Y, Z ), alpha5( X, Z ) }.
% 0.43/1.16 (426) {G0,W9,D3,L2,V3,M2} { ! alpha8( X, Y, Z ), !
% 0.43/1.16 unequally_directed_lines( X, line_connecting( Y, Z ) ) }.
% 0.43/1.16 (427) {G0,W12,D3,L3,V3,M3} { ! alpha5( X, Z ), unequally_directed_lines( X
% 0.43/1.16 , line_connecting( Y, Z ) ), alpha8( X, Y, Z ) }.
% 0.43/1.16 (428) {G0,W6,D2,L2,V2,M2} { ! alpha5( X, Y ), ! left_apart_point( Y, X )
% 0.43/1.16 }.
% 0.43/1.16 (429) {G0,W7,D3,L2,V2,M2} { ! alpha5( X, Y ), ! left_apart_point( Y,
% 0.43/1.16 reverse_line( X ) ) }.
% 0.43/1.16 (430) {G0,W10,D3,L3,V2,M3} { left_apart_point( Y, X ), left_apart_point( Y
% 0.43/1.16 , reverse_line( X ) ), alpha5( X, Y ) }.
% 0.43/1.16 (431) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), ! left_apart_point( Y, X )
% 0.43/1.16 }.
% 0.43/1.16 (432) {G0,W7,D3,L2,V2,M2} { ! alpha2( X, Y ), ! left_apart_point( Y,
% 0.43/1.16 reverse_line( X ) ) }.
% 0.43/1.16 (433) {G0,W10,D3,L3,V2,M3} { left_apart_point( Y, X ), left_apart_point( Y
% 0.43/1.16 , reverse_line( X ) ), alpha2( X, Y ) }.
% 0.43/1.16 (434) {G0,W15,D2,L3,V4,M3} { ! between_on_line( X, Y, Z, T ), alpha3( X, Y
% 0.43/1.16 , Z, T ), alpha6( X, Y, Z, T ) }.
% 0.43/1.16 (435) {G0,W10,D2,L2,V4,M2} { ! alpha3( X, Y, Z, T ), between_on_line( X, Y
% 0.43/1.16 , Z, T ) }.
% 0.43/1.16 (436) {G0,W10,D2,L2,V4,M2} { ! alpha6( X, Y, Z, T ), between_on_line( X, Y
% 0.43/1.16 , Z, T ) }.
% 0.43/1.16 (437) {G0,W9,D2,L2,V4,M2} { ! alpha6( X, Y, Z, T ), before_on_line( X, T,
% 0.43/1.16 Z ) }.
% 0.43/1.16 (438) {G0,W9,D2,L2,V4,M2} { ! alpha6( X, Y, Z, T ), before_on_line( X, Z,
% 0.43/1.16 Y ) }.
% 0.43/1.16 (439) {G0,W13,D2,L3,V4,M3} { ! before_on_line( X, T, Z ), ! before_on_line
% 0.43/1.16 ( X, Z, Y ), alpha6( X, Y, Z, T ) }.
% 0.43/1.16 (440) {G0,W9,D2,L2,V4,M2} { ! alpha3( X, Y, Z, T ), before_on_line( X, Y,
% 0.43/1.16 Z ) }.
% 0.43/1.16 (441) {G0,W9,D2,L2,V4,M2} { ! alpha3( X, Y, Z, T ), before_on_line( X, Z,
% 0.43/1.16 T ) }.
% 0.43/1.16 (442) {G0,W13,D2,L3,V4,M3} { ! before_on_line( X, Y, Z ), ! before_on_line
% 0.43/1.16 ( X, Z, T ), alpha3( X, Y, Z, T ) }.
% 0.43/1.16 (443) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 0.43/1.16 (444) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 0.43/1.16 , Z ), distinct_points( Y, Z ) }.
% 0.43/1.16 (445) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.43/1.16 (446) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X, Z
% 0.43/1.16 ), distinct_lines( Y, Z ) }.
% 0.43/1.16 (447) {G0,W3,D2,L1,V1,M1} { ! unequally_directed_lines( X, X ) }.
% 0.43/1.16 (448) {G0,W9,D2,L3,V3,M3} { ! unequally_directed_lines( X, Y ),
% 0.43/1.16 unequally_directed_lines( X, Z ), unequally_directed_lines( Y, Z ) }.
% 0.43/1.16 (449) {G0,W13,D3,L4,V3,M4} { ! unequally_directed_lines( X, Y ), !
% 0.43/1.16 unequally_directed_lines( X, reverse_line( Y ) ), alpha9( X, Z ),
% 0.43/1.16 unequally_directed_lines( Y, Z ) }.
% 0.43/1.16 (450) {G0,W14,D3,L4,V3,M4} { ! unequally_directed_lines( X, Y ), !
% 0.43/1.16 unequally_directed_lines( X, reverse_line( Y ) ), alpha9( X, Z ),
% 0.43/1.16 unequally_directed_lines( Y, reverse_line( Z ) ) }.
% 0.43/1.16 (451) {G0,W6,D2,L2,V2,M2} { ! alpha9( X, Y ), unequally_directed_lines( X
% 0.43/1.16 , Y ) }.
% 0.43/1.16 (452) {G0,W7,D3,L2,V2,M2} { ! alpha9( X, Y ), unequally_directed_lines( X
% 0.43/1.16 , reverse_line( Y ) ) }.
% 0.43/1.16 (453) {G0,W10,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y ), !
% 0.43/1.16 unequally_directed_lines( X, reverse_line( Y ) ), alpha9( X, Y ) }.
% 0.43/1.16 (454) {G0,W11,D3,L4,V2,M4} { ! line( X ), ! line( Y ),
% 0.43/1.16 unequally_directed_lines( X, Y ), unequally_directed_lines( X,
% 0.43/1.16 reverse_line( Y ) ) }.
% 0.43/1.16 (455) {G0,W14,D3,L4,V2,M4} { ! unequally_directed_lines( X, Y ), !
% 0.43/1.16 unequally_directed_lines( X, reverse_line( Y ) ), left_convergent_lines(
% 0.43/1.16 X, Y ), left_convergent_lines( X, reverse_line( Y ) ) }.
% 0.43/1.16 (456) {G0,W3,D2,L1,V2,M1} { ! left_apart_point( X, Y ) }.
% 0.43/1.16 (457) {G0,W4,D3,L1,V2,M1} { ! left_apart_point( X, reverse_line( Y ) ) }.
% 0.43/1.16 (458) {G0,W3,D2,L1,V2,M1} { ! left_convergent_lines( X, Y ) }.
% 0.43/1.16 (459) {G0,W4,D3,L1,V2,M1} { ! left_convergent_lines( X, reverse_line( Y )
% 0.43/1.16 ) }.
% 0.43/1.16 (460) {G0,W11,D3,L4,V2,M4} { ! point( X ), ! point( Y ), ! distinct_points
% 0.43/1.16 ( X, Y ), line( line_connecting( X, Y ) ) }.
% 0.43/1.16 (461) {G0,W15,D3,L5,V2,M5} { ! line( X ), ! line( Y ), !
% 0.43/1.16 unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.43/1.16 reverse_line( Y ) ), point( intersection_point( X, Y ) ) }.
% 0.43/1.16 (462) {G0,W8,D3,L3,V2,M3} { ! point( Y ), ! line( X ), line(
% 0.43/1.16 parallel_through_point( X, Y ) ) }.
% 0.43/1.16 (463) {G0,W5,D3,L2,V1,M2} { ! line( X ), line( reverse_line( X ) ) }.
% 0.43/1.16 (464) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.43/1.16 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 0.43/1.16 (465) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.43/1.16 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 0.43/1.16 (466) {G0,W12,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y ), !
% 0.43/1.16 unequally_directed_lines( X, reverse_line( Y ) ), ! apart_point_and_line
% 0.43/1.16 ( intersection_point( X, Y ), X ) }.
% 0.43/1.16 (467) {G0,W12,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y ), !
% 0.43/1.16 unequally_directed_lines( X, reverse_line( Y ) ), ! apart_point_and_line
% 0.43/1.16 ( intersection_point( X, Y ), Y ) }.
% 0.43/1.16 (468) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.43/1.16 parallel_through_point( Y, X ) ) }.
% 0.43/1.16 (469) {G0,W4,D3,L1,V1,M1} { ! distinct_lines( X, reverse_line( X ) ) }.
% 0.43/1.16 (470) {G0,W8,D4,L1,V2,M1} { ! unequally_directed_lines( line_connecting( X
% 0.43/1.16 , Y ), reverse_line( line_connecting( Y, X ) ) ) }.
% 0.43/1.16 (471) {G0,W5,D3,L1,V2,M1} { ! unequally_directed_lines(
% 0.43/1.16 parallel_through_point( Y, X ), Y ) }.
% 0.43/1.16 (472) {G0,W34,D3,L10,V4,M10} { ! distinct_points( X, Y ), ! distinct_lines
% 0.43/1.16 ( Z, T ), left_apart_point( X, Z ), left_apart_point( Y, Z ),
% 0.43/1.16 left_apart_point( X, T ), left_apart_point( Y, T ), left_apart_point( X,
% 0.43/1.16 reverse_line( Z ) ), left_apart_point( Y, reverse_line( Z ) ),
% 0.43/1.16 left_apart_point( X, reverse_line( T ) ), left_apart_point( Y,
% 0.43/1.16 reverse_line( T ) ) }.
% 0.43/1.16 (473) {G0,W14,D3,L4,V3,M4} { ! distinct_points( X, Y ), ! left_apart_point
% 0.43/1.16 ( X, Z ), left_apart_point( Y, Z ), left_convergent_lines(
% 0.43/1.16 line_connecting( X, Y ), Z ) }.
% 0.43/1.16 (474) {G0,W9,D2,L3,V3,M3} { ! left_apart_point( X, Y ), distinct_points( X
% 0.43/1.16 , Z ), left_apart_point( Z, Y ) }.
% 0.43/1.16 (475) {G0,W13,D3,L4,V3,M4} { ! left_apart_point( X, Y ), !
% 0.43/1.16 unequally_directed_lines( Y, Z ), distinct_lines( Y, Z ),
% 0.43/1.16 left_apart_point( X, reverse_line( Z ) ) }.
% 0.43/1.16 (476) {G0,W9,D2,L3,V3,M3} { ! left_convergent_lines( X, Y ),
% 0.43/1.16 unequally_directed_lines( Y, Z ), left_convergent_lines( X, Z ) }.
% 0.43/1.16 (477) {G0,W10,D3,L3,V0,M3} { alpha10( skol1, skol2 ), !
% 0.43/1.16 unequally_directed_lines( skol1, skol2 ), ! unequally_directed_lines(
% 0.43/1.16 skol1, reverse_line( skol2 ) ) }.
% 0.43/1.16 (478) {G0,W6,D2,L2,V0,M2} { alpha10( skol1, skol2 ), convergent_lines(
% 0.43/1.16 skol1, skol2 ) }.
% 0.43/1.16 (479) {G0,W6,D2,L2,V2,M2} { ! alpha10( X, Y ), ! convergent_lines( X, Y )
% 0.43/1.16 }.
% 0.43/1.16 (480) {G0,W6,D2,L2,V2,M2} { ! alpha10( X, Y ), unequally_directed_lines( X
% 0.43/1.16 , Y ) }.
% 0.43/1.16 (481) {G0,W7,D3,L2,V2,M2} { ! alpha10( X, Y ), unequally_directed_lines( X
% 0.43/1.16 , reverse_line( Y ) ) }.
% 0.43/1.16 (482) {G0,W13,D3,L4,V2,M4} { convergent_lines( X, Y ), !
% 0.43/1.16 unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.43/1.16 reverse_line( Y ) ), alpha10( X, Y ) }.
% 0.43/1.16
% 0.43/1.16
% 0.43/1.16 Total Proof:
% 0.43/1.16
% 0.43/1.16 subsumption: (3) {G0,W6,D2,L2,V2,M1} I { ! convergent_lines( X, Y ),
% 0.43/1.16 unequally_directed_lines( X, Y ) }.
% 0.43/1.16 parent0: (407) {G0,W6,D2,L2,V2,M2} { ! convergent_lines( X, Y ),
% 0.43/1.16 unequally_directed_lines( X, Y ) }.
% 0.43/1.16 substitution0:
% 0.43/1.16 X := X
% 0.43/1.16 Y := Y
% 0.43/1.16 end
% 0.43/1.16 permutation0:
% 0.43/1.16 0 ==> 0
% 0.43/1.16 1 ==> 1
% 0.43/1.16 end
% 0.43/1.16
% 0.43/1.16 subsumption: (4) {G0,W7,D3,L2,V2,M1} I { ! convergent_lines( X, Y ),
% 0.43/1.16 unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.43/1.16 parent0: (408) {G0,W7,D3,L2,V2,M2} { ! convergent_lines( X, Y ),
% 0.43/1.16 unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.43/1.16 substitution0:
% 0.43/1.16 X := X
% 0.43/1.16 Y := Y
% 0.43/1.16 end
% 0.43/1.16 permutation0:
% 0.43/1.16 0 ==> 0
% 0.43/1.16 1 ==> 1
% 0.43/1.16 end
% 0.43/1.16
% 0.43/1.16 subsumption: (5) {G0,W10,D3,L3,V2,M2} I { convergent_lines( X, Y ), !
% 0.43/1.16 unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.43/1.16 reverse_line( Y ) ) }.
% 0.43/1.16 parent0: (409) {G0,W10,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y ),
% 0.43/1.16 ! unequally_directed_lines( X, reverse_line( Y ) ), convergent_lines( X,
% 0.43/1.16 Y ) }.
% 0.43/1.16 substitution0:
% 0.43/1.16 X := X
% 0.43/1.16 Y := Y
% 0.43/1.16 end
% 0.43/1.16 permutation0:
% 0.43/1.16 0 ==> 1
% 0.43/1.16 1 ==> 2
% 0.43/1.16 2 ==> 0
% 0.43/1.16 end
% 0.43/1.16
% 0.43/1.16 subsumption: (43) {G0,W3,D2,L1,V1,M1} I { ! unequally_directed_lines( X, X
% 0.43/1.16 ) }.
% 0.43/1.16 parent0: (447) {G0,W3,D2,L1,V1,M1} { ! unequally_directed_lines( X, X )
% 0.43/1.16 }.
% 0.43/1.16 substitution0:
% 0.43/1.16 X := X
% 0.43/1.16 end
% 0.43/1.16 permutation0:
% 0.43/1.16 0 ==> 0
% 0.43/1.16 end
% 0.43/1.16
% 0.43/1.16 subsumption: (44) {G0,W9,D2,L3,V3,M3} I { unequally_directed_lines( X, Z )
% 0.43/1.16 , unequally_directed_lines( Y, Z ), ! unequally_directed_lines( X, Y )
% 0.43/1.16 }.
% 0.43/1.16 parent0: (448) {G0,W9,D2,L3,V3,M3} { ! unequally_directed_lines( X, Y ),
% 0.43/1.16 unequally_directed_lines( X, Z ), unequally_directed_lines( Y, Z ) }.
% 0.43/1.16 substitution0:
% 0.43/1.16 X := X
% 0.43/1.16 Y := Y
% 0.43/1.16 Z := Z
% 0.43/1.16 end
% 0.43/1.16 permutation0:
% 0.43/1.16 0 ==> 2
% 0.43/1.16 1 ==> 0
% 0.43/1.16 2 ==> 1
% 0.43/1.16 end
% 0.43/1.16
% 0.43/1.16 subsumption: (51) {G0,W14,D3,L4,V2,M2} I { ! unequally_directed_lines( X, Y
% 0.43/1.16 ), ! unequally_directed_lines( X, reverse_line( Y ) ),
% 0.43/1.16 left_convergent_lines( X, reverse_line( Y ) ), left_convergent_lines( X,
% 0.43/1.16 Y ) }.
% 0.43/1.16 parent0: (455) {G0,W14,D3,L4,V2,M4} { ! unequally_directed_lines( X, Y ),
% 0.43/1.16 ! unequally_directed_lines( X, reverse_line( Y ) ), left_convergent_lines
% 0.43/1.16 ( X, Y ), left_convergent_lines( X, reverse_line( Y ) ) }.
% 0.43/1.16 substitution0:
% 0.43/1.16 X := X
% 0.43/1.16 Y := Y
% 0.43/1.16 end
% 0.43/1.16 permutation0:
% 0.43/1.16 0 ==> 0
% 0.43/1.16 1 ==> 1
% 0.43/1.16 2 ==> 3
% 0.43/1.16 3 ==> 2
% 0.43/1.16 end
% 0.43/1.16
% 0.43/1.16 subsumption: (53) {G0,W3,D2,L1,V2,M1} I { ! left_convergent_lines( X, Y )
% 0.43/1.16 }.
% 0.43/1.16 parent0: (458) {G0,W3,D2,L1,V2,M1} { ! left_convergent_lines( X, Y ) }.
% 0.43/1.16 substitution0:
% 0.43/1.16 X := X
% 0.43/1.16 Y := Y
% 0.43/1.16 end
% 0.43/1.16 permutation0:
% 0.43/1.16 0 ==> 0
% 0.43/1.16 end
% 0.43/1.16
% 0.43/1.16 subsumption: (65) {G0,W5,D3,L1,V2,M1} I { ! unequally_directed_lines(
% 0.43/1.16 parallel_through_point( Y, X ), Y ) }.
% 0.43/1.16 parent0: (471) {G0,W5,D3,L1,V2,M1} { ! unequally_directed_lines(
% 0.43/1.16 parallel_through_point( Y, X ), Y ) }.
% 0.43/1.16 substitution0:
% 0.43/1.16 X := X
% 0.43/1.16 Y := Y
% 0.43/1.16 end
% 0.43/1.16 permutation0:
% 0.43/1.16 0 ==> 0
% 0.43/1.16 end
% 0.43/1.16
% 0.43/1.16 subsumption: (68) {G0,W6,D2,L2,V0,M1} I { convergent_lines( skol1, skol2 )
% 0.43/1.16 , alpha10( skol1, skol2 ) }.
% 0.43/1.16 parent0: (478) {G0,W6,D2,L2,V0,M2} { alpha10( skol1, skol2 ),
% 0.43/1.17 convergent_lines( skol1, skol2 ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 end
% 0.43/1.17 permutation0:
% 0.43/1.17 0 ==> 1
% 0.43/1.17 1 ==> 0
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 subsumption: (70) {G0,W6,D2,L2,V2,M1} I { unequally_directed_lines( X, Y )
% 0.43/1.17 , ! alpha10( X, Y ) }.
% 0.43/1.17 parent0: (480) {G0,W6,D2,L2,V2,M2} { ! alpha10( X, Y ),
% 0.43/1.17 unequally_directed_lines( X, Y ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 X := X
% 0.43/1.17 Y := Y
% 0.43/1.17 end
% 0.43/1.17 permutation0:
% 0.43/1.17 0 ==> 1
% 0.43/1.17 1 ==> 0
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 subsumption: (71) {G0,W7,D3,L2,V2,M1} I { unequally_directed_lines( X,
% 0.43/1.17 reverse_line( Y ) ), ! alpha10( X, Y ) }.
% 0.43/1.17 parent0: (481) {G0,W7,D3,L2,V2,M2} { ! alpha10( X, Y ),
% 0.43/1.17 unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 X := X
% 0.43/1.17 Y := Y
% 0.43/1.17 end
% 0.43/1.17 permutation0:
% 0.43/1.17 0 ==> 1
% 0.43/1.17 1 ==> 0
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 resolution: (614) {G1,W6,D2,L2,V0,M2} { unequally_directed_lines( skol1,
% 0.43/1.17 skol2 ), convergent_lines( skol1, skol2 ) }.
% 0.43/1.17 parent0[1]: (70) {G0,W6,D2,L2,V2,M1} I { unequally_directed_lines( X, Y ),
% 0.43/1.17 ! alpha10( X, Y ) }.
% 0.43/1.17 parent1[1]: (68) {G0,W6,D2,L2,V0,M1} I { convergent_lines( skol1, skol2 ),
% 0.43/1.17 alpha10( skol1, skol2 ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 X := skol1
% 0.43/1.17 Y := skol2
% 0.43/1.17 end
% 0.43/1.17 substitution1:
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 resolution: (615) {G1,W6,D2,L2,V0,M2} { unequally_directed_lines( skol1,
% 0.43/1.17 skol2 ), unequally_directed_lines( skol1, skol2 ) }.
% 0.43/1.17 parent0[0]: (3) {G0,W6,D2,L2,V2,M1} I { ! convergent_lines( X, Y ),
% 0.43/1.17 unequally_directed_lines( X, Y ) }.
% 0.43/1.17 parent1[1]: (614) {G1,W6,D2,L2,V0,M2} { unequally_directed_lines( skol1,
% 0.43/1.17 skol2 ), convergent_lines( skol1, skol2 ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 X := skol1
% 0.43/1.17 Y := skol2
% 0.43/1.17 end
% 0.43/1.17 substitution1:
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 factor: (616) {G1,W3,D2,L1,V0,M1} { unequally_directed_lines( skol1, skol2
% 0.43/1.17 ) }.
% 0.43/1.17 parent0[0, 1]: (615) {G1,W6,D2,L2,V0,M2} { unequally_directed_lines( skol1
% 0.43/1.17 , skol2 ), unequally_directed_lines( skol1, skol2 ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 subsumption: (81) {G1,W3,D2,L1,V0,M1} R(68,70);r(3) {
% 0.43/1.17 unequally_directed_lines( skol1, skol2 ) }.
% 0.43/1.17 parent0: (616) {G1,W3,D2,L1,V0,M1} { unequally_directed_lines( skol1,
% 0.43/1.17 skol2 ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 end
% 0.43/1.17 permutation0:
% 0.43/1.17 0 ==> 0
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 resolution: (617) {G1,W7,D3,L2,V0,M2} { convergent_lines( skol1, skol2 ),
% 0.43/1.17 ! unequally_directed_lines( skol1, reverse_line( skol2 ) ) }.
% 0.43/1.17 parent0[1]: (5) {G0,W10,D3,L3,V2,M2} I { convergent_lines( X, Y ), !
% 0.43/1.17 unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.43/1.17 reverse_line( Y ) ) }.
% 0.43/1.17 parent1[0]: (81) {G1,W3,D2,L1,V0,M1} R(68,70);r(3) {
% 0.43/1.17 unequally_directed_lines( skol1, skol2 ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 X := skol1
% 0.43/1.17 Y := skol2
% 0.43/1.17 end
% 0.43/1.17 substitution1:
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 subsumption: (82) {G2,W7,D3,L2,V0,M1} R(5,81) { convergent_lines( skol1,
% 0.43/1.17 skol2 ), ! unequally_directed_lines( skol1, reverse_line( skol2 ) ) }.
% 0.43/1.17 parent0: (617) {G1,W7,D3,L2,V0,M2} { convergent_lines( skol1, skol2 ), !
% 0.43/1.17 unequally_directed_lines( skol1, reverse_line( skol2 ) ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 end
% 0.43/1.17 permutation0:
% 0.43/1.17 0 ==> 0
% 0.43/1.17 1 ==> 1
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 resolution: (618) {G1,W7,D3,L2,V0,M2} { unequally_directed_lines( skol1,
% 0.43/1.17 reverse_line( skol2 ) ), convergent_lines( skol1, skol2 ) }.
% 0.43/1.17 parent0[1]: (71) {G0,W7,D3,L2,V2,M1} I { unequally_directed_lines( X,
% 0.43/1.17 reverse_line( Y ) ), ! alpha10( X, Y ) }.
% 0.43/1.17 parent1[1]: (68) {G0,W6,D2,L2,V0,M1} I { convergent_lines( skol1, skol2 ),
% 0.43/1.17 alpha10( skol1, skol2 ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 X := skol1
% 0.43/1.17 Y := skol2
% 0.43/1.17 end
% 0.43/1.17 substitution1:
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 resolution: (619) {G2,W6,D2,L2,V0,M2} { convergent_lines( skol1, skol2 ),
% 0.43/1.17 convergent_lines( skol1, skol2 ) }.
% 0.43/1.17 parent0[1]: (82) {G2,W7,D3,L2,V0,M1} R(5,81) { convergent_lines( skol1,
% 0.43/1.17 skol2 ), ! unequally_directed_lines( skol1, reverse_line( skol2 ) ) }.
% 0.43/1.17 parent1[0]: (618) {G1,W7,D3,L2,V0,M2} { unequally_directed_lines( skol1,
% 0.43/1.17 reverse_line( skol2 ) ), convergent_lines( skol1, skol2 ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 end
% 0.43/1.17 substitution1:
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 factor: (620) {G2,W3,D2,L1,V0,M1} { convergent_lines( skol1, skol2 ) }.
% 0.43/1.17 parent0[0, 1]: (619) {G2,W6,D2,L2,V0,M2} { convergent_lines( skol1, skol2
% 0.43/1.17 ), convergent_lines( skol1, skol2 ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 subsumption: (91) {G3,W3,D2,L1,V0,M1} R(71,68);r(82) { convergent_lines(
% 0.43/1.17 skol1, skol2 ) }.
% 0.43/1.17 parent0: (620) {G2,W3,D2,L1,V0,M1} { convergent_lines( skol1, skol2 ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 end
% 0.43/1.17 permutation0:
% 0.43/1.17 0 ==> 0
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 resolution: (621) {G1,W6,D2,L2,V2,M2} { unequally_directed_lines( Y, X ),
% 0.43/1.17 ! unequally_directed_lines( X, Y ) }.
% 0.43/1.17 parent0[0]: (43) {G0,W3,D2,L1,V1,M1} I { ! unequally_directed_lines( X, X )
% 0.43/1.17 }.
% 0.43/1.17 parent1[0]: (44) {G0,W9,D2,L3,V3,M3} I { unequally_directed_lines( X, Z ),
% 0.43/1.17 unequally_directed_lines( Y, Z ), ! unequally_directed_lines( X, Y ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 X := X
% 0.43/1.17 end
% 0.43/1.17 substitution1:
% 0.43/1.17 X := X
% 0.43/1.17 Y := Y
% 0.43/1.17 Z := X
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 subsumption: (115) {G1,W6,D2,L2,V2,M2} R(44,43) { !
% 0.43/1.17 unequally_directed_lines( Y, X ), unequally_directed_lines( X, Y ) }.
% 0.43/1.17 parent0: (621) {G1,W6,D2,L2,V2,M2} { unequally_directed_lines( Y, X ), !
% 0.43/1.17 unequally_directed_lines( X, Y ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 X := Y
% 0.43/1.17 Y := X
% 0.43/1.17 end
% 0.43/1.17 permutation0:
% 0.43/1.17 0 ==> 1
% 0.43/1.17 1 ==> 0
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 resolution: (623) {G1,W5,D3,L1,V2,M1} { ! unequally_directed_lines( X,
% 0.43/1.17 parallel_through_point( X, Y ) ) }.
% 0.43/1.17 parent0[0]: (65) {G0,W5,D3,L1,V2,M1} I { ! unequally_directed_lines(
% 0.43/1.17 parallel_through_point( Y, X ), Y ) }.
% 0.43/1.17 parent1[1]: (115) {G1,W6,D2,L2,V2,M2} R(44,43) { ! unequally_directed_lines
% 0.43/1.17 ( Y, X ), unequally_directed_lines( X, Y ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 X := Y
% 0.43/1.17 Y := X
% 0.43/1.17 end
% 0.43/1.17 substitution1:
% 0.43/1.17 X := parallel_through_point( X, Y )
% 0.43/1.17 Y := X
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 subsumption: (127) {G2,W5,D3,L1,V2,M1} R(115,65) { !
% 0.43/1.17 unequally_directed_lines( X, parallel_through_point( X, Y ) ) }.
% 0.43/1.17 parent0: (623) {G1,W5,D3,L1,V2,M1} { ! unequally_directed_lines( X,
% 0.43/1.17 parallel_through_point( X, Y ) ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 X := X
% 0.43/1.17 Y := Y
% 0.43/1.17 end
% 0.43/1.17 permutation0:
% 0.43/1.17 0 ==> 0
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 resolution: (624) {G1,W8,D3,L2,V3,M2} { unequally_directed_lines( Z,
% 0.43/1.17 parallel_through_point( X, Y ) ), ! unequally_directed_lines( X, Z ) }.
% 0.43/1.17 parent0[0]: (127) {G2,W5,D3,L1,V2,M1} R(115,65) { !
% 0.43/1.17 unequally_directed_lines( X, parallel_through_point( X, Y ) ) }.
% 0.43/1.17 parent1[0]: (44) {G0,W9,D2,L3,V3,M3} I { unequally_directed_lines( X, Z ),
% 0.43/1.17 unequally_directed_lines( Y, Z ), ! unequally_directed_lines( X, Y ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 X := X
% 0.43/1.17 Y := Y
% 0.43/1.17 end
% 0.43/1.17 substitution1:
% 0.43/1.17 X := X
% 0.43/1.17 Y := Z
% 0.43/1.17 Z := parallel_through_point( X, Y )
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 subsumption: (129) {G3,W8,D3,L2,V3,M2} R(127,44) { !
% 0.43/1.17 unequally_directed_lines( Y, X ), unequally_directed_lines( X,
% 0.43/1.17 parallel_through_point( Y, Z ) ) }.
% 0.43/1.17 parent0: (624) {G1,W8,D3,L2,V3,M2} { unequally_directed_lines( Z,
% 0.43/1.17 parallel_through_point( X, Y ) ), ! unequally_directed_lines( X, Z ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 X := Y
% 0.43/1.17 Y := Z
% 0.43/1.17 Z := X
% 0.43/1.17 end
% 0.43/1.17 permutation0:
% 0.43/1.17 0 ==> 1
% 0.43/1.17 1 ==> 0
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 resolution: (627) {G2,W8,D3,L2,V3,M2} { unequally_directed_lines(
% 0.43/1.17 parallel_through_point( Y, Z ), X ), ! unequally_directed_lines( Y, X )
% 0.43/1.17 }.
% 0.43/1.17 parent0[0]: (115) {G1,W6,D2,L2,V2,M2} R(44,43) { ! unequally_directed_lines
% 0.43/1.17 ( Y, X ), unequally_directed_lines( X, Y ) }.
% 0.43/1.17 parent1[1]: (129) {G3,W8,D3,L2,V3,M2} R(127,44) { !
% 0.43/1.17 unequally_directed_lines( Y, X ), unequally_directed_lines( X,
% 0.43/1.17 parallel_through_point( Y, Z ) ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 X := parallel_through_point( Y, Z )
% 0.43/1.17 Y := X
% 0.43/1.17 end
% 0.43/1.17 substitution1:
% 0.43/1.17 X := X
% 0.43/1.17 Y := Y
% 0.43/1.17 Z := Z
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 subsumption: (194) {G4,W8,D3,L2,V3,M2} R(129,115) {
% 0.43/1.17 unequally_directed_lines( parallel_through_point( X, Z ), Y ), !
% 0.43/1.17 unequally_directed_lines( X, Y ) }.
% 0.43/1.17 parent0: (627) {G2,W8,D3,L2,V3,M2} { unequally_directed_lines(
% 0.43/1.17 parallel_through_point( Y, Z ), X ), ! unequally_directed_lines( Y, X )
% 0.43/1.17 }.
% 0.43/1.17 substitution0:
% 0.43/1.17 X := Y
% 0.43/1.17 Y := X
% 0.43/1.17 Z := Z
% 0.43/1.17 end
% 0.43/1.17 permutation0:
% 0.43/1.17 0 ==> 0
% 0.43/1.17 1 ==> 1
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 resolution: (628) {G1,W9,D3,L2,V3,M2} { unequally_directed_lines(
% 0.43/1.17 parallel_through_point( X, Y ), reverse_line( Z ) ), ! convergent_lines(
% 0.43/1.17 X, Z ) }.
% 0.43/1.17 parent0[1]: (194) {G4,W8,D3,L2,V3,M2} R(129,115) { unequally_directed_lines
% 0.43/1.17 ( parallel_through_point( X, Z ), Y ), ! unequally_directed_lines( X, Y )
% 0.43/1.17 }.
% 0.43/1.17 parent1[1]: (4) {G0,W7,D3,L2,V2,M1} I { ! convergent_lines( X, Y ),
% 0.43/1.17 unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 X := X
% 0.43/1.17 Y := reverse_line( Z )
% 0.43/1.17 Z := Y
% 0.43/1.17 end
% 0.43/1.17 substitution1:
% 0.43/1.17 X := X
% 0.43/1.17 Y := Z
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 subsumption: (262) {G5,W9,D3,L2,V3,M1} R(194,4) { ! convergent_lines( X, Z
% 0.43/1.17 ), unequally_directed_lines( parallel_through_point( X, Y ),
% 0.43/1.17 reverse_line( Z ) ) }.
% 0.43/1.17 parent0: (628) {G1,W9,D3,L2,V3,M2} { unequally_directed_lines(
% 0.43/1.17 parallel_through_point( X, Y ), reverse_line( Z ) ), ! convergent_lines(
% 0.43/1.17 X, Z ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 X := X
% 0.43/1.17 Y := Y
% 0.43/1.17 Z := Z
% 0.43/1.17 end
% 0.43/1.17 permutation0:
% 0.43/1.17 0 ==> 1
% 0.43/1.17 1 ==> 0
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 resolution: (629) {G1,W8,D3,L2,V3,M2} { unequally_directed_lines(
% 0.43/1.17 parallel_through_point( X, Y ), Z ), ! convergent_lines( X, Z ) }.
% 0.43/1.17 parent0[1]: (194) {G4,W8,D3,L2,V3,M2} R(129,115) { unequally_directed_lines
% 0.43/1.17 ( parallel_through_point( X, Z ), Y ), ! unequally_directed_lines( X, Y )
% 0.43/1.17 }.
% 0.43/1.17 parent1[1]: (3) {G0,W6,D2,L2,V2,M1} I { ! convergent_lines( X, Y ),
% 0.43/1.17 unequally_directed_lines( X, Y ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 X := X
% 0.43/1.17 Y := Z
% 0.43/1.17 Z := Y
% 0.43/1.17 end
% 0.43/1.17 substitution1:
% 0.43/1.17 X := X
% 0.43/1.17 Y := Z
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 subsumption: (263) {G5,W8,D3,L2,V3,M1} R(194,3) { ! convergent_lines( X, Z
% 0.43/1.17 ), unequally_directed_lines( parallel_through_point( X, Y ), Z ) }.
% 0.43/1.17 parent0: (629) {G1,W8,D3,L2,V3,M2} { unequally_directed_lines(
% 0.43/1.17 parallel_through_point( X, Y ), Z ), ! convergent_lines( X, Z ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 X := X
% 0.43/1.17 Y := Y
% 0.43/1.17 Z := Z
% 0.43/1.17 end
% 0.43/1.17 permutation0:
% 0.43/1.17 0 ==> 1
% 0.43/1.17 1 ==> 0
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 resolution: (631) {G1,W14,D3,L3,V3,M3} { convergent_lines(
% 0.43/1.17 parallel_through_point( X, Y ), Z ), ! unequally_directed_lines(
% 0.43/1.17 parallel_through_point( X, Y ), reverse_line( Z ) ), ! convergent_lines(
% 0.43/1.17 X, Z ) }.
% 0.43/1.17 parent0[1]: (5) {G0,W10,D3,L3,V2,M2} I { convergent_lines( X, Y ), !
% 0.43/1.17 unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.43/1.17 reverse_line( Y ) ) }.
% 0.43/1.17 parent1[1]: (263) {G5,W8,D3,L2,V3,M1} R(194,3) { ! convergent_lines( X, Z )
% 0.43/1.17 , unequally_directed_lines( parallel_through_point( X, Y ), Z ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 X := parallel_through_point( X, Y )
% 0.43/1.17 Y := Z
% 0.43/1.17 end
% 0.43/1.17 substitution1:
% 0.43/1.17 X := X
% 0.43/1.17 Y := Y
% 0.43/1.17 Z := Z
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 resolution: (633) {G2,W11,D3,L3,V3,M3} { convergent_lines(
% 0.43/1.17 parallel_through_point( X, Y ), Z ), ! convergent_lines( X, Z ), !
% 0.43/1.17 convergent_lines( X, Z ) }.
% 0.43/1.17 parent0[1]: (631) {G1,W14,D3,L3,V3,M3} { convergent_lines(
% 0.43/1.17 parallel_through_point( X, Y ), Z ), ! unequally_directed_lines(
% 0.43/1.17 parallel_through_point( X, Y ), reverse_line( Z ) ), ! convergent_lines(
% 0.43/1.17 X, Z ) }.
% 0.43/1.17 parent1[1]: (262) {G5,W9,D3,L2,V3,M1} R(194,4) { ! convergent_lines( X, Z )
% 0.43/1.17 , unequally_directed_lines( parallel_through_point( X, Y ), reverse_line
% 0.43/1.17 ( Z ) ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 X := X
% 0.43/1.17 Y := Y
% 0.43/1.17 Z := Z
% 0.43/1.17 end
% 0.43/1.17 substitution1:
% 0.43/1.17 X := X
% 0.43/1.17 Y := Y
% 0.43/1.17 Z := Z
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 factor: (634) {G2,W8,D3,L2,V3,M2} { convergent_lines(
% 0.43/1.17 parallel_through_point( X, Y ), Z ), ! convergent_lines( X, Z ) }.
% 0.43/1.17 parent0[1, 2]: (633) {G2,W11,D3,L3,V3,M3} { convergent_lines(
% 0.43/1.17 parallel_through_point( X, Y ), Z ), ! convergent_lines( X, Z ), !
% 0.43/1.17 convergent_lines( X, Z ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 X := X
% 0.43/1.17 Y := Y
% 0.43/1.17 Z := Z
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 subsumption: (354) {G6,W8,D3,L2,V3,M2} R(263,5);r(262) { convergent_lines(
% 0.43/1.17 parallel_through_point( X, Z ), Y ), ! convergent_lines( X, Y ) }.
% 0.43/1.17 parent0: (634) {G2,W8,D3,L2,V3,M2} { convergent_lines(
% 0.43/1.17 parallel_through_point( X, Y ), Z ), ! convergent_lines( X, Z ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 X := X
% 0.43/1.17 Y := Z
% 0.43/1.17 Z := Y
% 0.43/1.17 end
% 0.43/1.17 permutation0:
% 0.43/1.17 0 ==> 0
% 0.43/1.17 1 ==> 1
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 resolution: (635) {G4,W5,D3,L1,V1,M1} { convergent_lines(
% 0.43/1.17 parallel_through_point( skol1, X ), skol2 ) }.
% 0.43/1.17 parent0[1]: (354) {G6,W8,D3,L2,V3,M2} R(263,5);r(262) { convergent_lines(
% 0.43/1.17 parallel_through_point( X, Z ), Y ), ! convergent_lines( X, Y ) }.
% 0.43/1.17 parent1[0]: (91) {G3,W3,D2,L1,V0,M1} R(71,68);r(82) { convergent_lines(
% 0.43/1.17 skol1, skol2 ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 X := skol1
% 0.43/1.17 Y := skol2
% 0.43/1.17 Z := X
% 0.43/1.17 end
% 0.43/1.17 substitution1:
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 subsumption: (357) {G7,W5,D3,L1,V1,M1} R(354,91) { convergent_lines(
% 0.43/1.17 parallel_through_point( skol1, X ), skol2 ) }.
% 0.43/1.17 parent0: (635) {G4,W5,D3,L1,V1,M1} { convergent_lines(
% 0.43/1.17 parallel_through_point( skol1, X ), skol2 ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 X := X
% 0.43/1.17 end
% 0.43/1.17 permutation0:
% 0.43/1.17 0 ==> 0
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 resolution: (636) {G7,W7,D4,L1,V2,M1} { convergent_lines(
% 0.43/1.17 parallel_through_point( parallel_through_point( skol1, X ), Y ), skol2 )
% 0.43/1.17 }.
% 0.43/1.17 parent0[1]: (354) {G6,W8,D3,L2,V3,M2} R(263,5);r(262) { convergent_lines(
% 0.43/1.17 parallel_through_point( X, Z ), Y ), ! convergent_lines( X, Y ) }.
% 0.43/1.17 parent1[0]: (357) {G7,W5,D3,L1,V1,M1} R(354,91) { convergent_lines(
% 0.43/1.17 parallel_through_point( skol1, X ), skol2 ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 X := parallel_through_point( skol1, X )
% 0.43/1.17 Y := skol2
% 0.43/1.17 Z := Y
% 0.43/1.17 end
% 0.43/1.17 substitution1:
% 0.43/1.17 X := X
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 subsumption: (358) {G8,W7,D4,L1,V2,M1} R(357,354) { convergent_lines(
% 0.43/1.17 parallel_through_point( parallel_through_point( skol1, X ), Y ), skol2 )
% 0.43/1.17 }.
% 0.43/1.17 parent0: (636) {G7,W7,D4,L1,V2,M1} { convergent_lines(
% 0.43/1.17 parallel_through_point( parallel_through_point( skol1, X ), Y ), skol2 )
% 0.43/1.17 }.
% 0.43/1.17 substitution0:
% 0.43/1.17 X := X
% 0.43/1.17 Y := Y
% 0.43/1.17 end
% 0.43/1.17 permutation0:
% 0.43/1.17 0 ==> 0
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 resolution: (637) {G1,W10,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y
% 0.43/1.17 ), ! unequally_directed_lines( X, reverse_line( Y ) ),
% 0.43/1.17 left_convergent_lines( X, Y ) }.
% 0.43/1.17 parent0[0]: (53) {G0,W3,D2,L1,V2,M1} I { ! left_convergent_lines( X, Y )
% 0.43/1.17 }.
% 0.43/1.17 parent1[2]: (51) {G0,W14,D3,L4,V2,M2} I { ! unequally_directed_lines( X, Y
% 0.43/1.17 ), ! unequally_directed_lines( X, reverse_line( Y ) ),
% 0.43/1.17 left_convergent_lines( X, reverse_line( Y ) ), left_convergent_lines( X,
% 0.43/1.17 Y ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 X := X
% 0.43/1.17 Y := reverse_line( Y )
% 0.43/1.17 end
% 0.43/1.17 substitution1:
% 0.43/1.17 X := X
% 0.43/1.17 Y := Y
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 resolution: (639) {G1,W7,D3,L2,V2,M2} { ! unequally_directed_lines( X, Y )
% 0.43/1.17 , ! unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.43/1.17 parent0[0]: (53) {G0,W3,D2,L1,V2,M1} I { ! left_convergent_lines( X, Y )
% 0.43/1.17 }.
% 0.43/1.17 parent1[2]: (637) {G1,W10,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y
% 0.43/1.17 ), ! unequally_directed_lines( X, reverse_line( Y ) ),
% 0.43/1.17 left_convergent_lines( X, Y ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 X := X
% 0.43/1.17 Y := Y
% 0.43/1.17 end
% 0.43/1.17 substitution1:
% 0.43/1.17 X := X
% 0.43/1.17 Y := Y
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 subsumption: (360) {G1,W7,D3,L2,V2,M2} S(51);r(53);r(53) { !
% 0.43/1.17 unequally_directed_lines( X, reverse_line( Y ) ), !
% 0.43/1.17 unequally_directed_lines( X, Y ) }.
% 0.43/1.17 parent0: (639) {G1,W7,D3,L2,V2,M2} { ! unequally_directed_lines( X, Y ), !
% 0.43/1.17 unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 X := X
% 0.43/1.17 Y := Y
% 0.43/1.17 end
% 0.43/1.17 permutation0:
% 0.43/1.17 0 ==> 1
% 0.43/1.17 1 ==> 0
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 resolution: (641) {G2,W9,D3,L2,V3,M2} { ! unequally_directed_lines(
% 0.43/1.17 parallel_through_point( X, Y ), reverse_line( Z ) ), ! convergent_lines(
% 0.43/1.17 X, Z ) }.
% 0.43/1.17 parent0[1]: (360) {G1,W7,D3,L2,V2,M2} S(51);r(53);r(53) { !
% 0.43/1.17 unequally_directed_lines( X, reverse_line( Y ) ), !
% 0.43/1.17 unequally_directed_lines( X, Y ) }.
% 0.43/1.17 parent1[1]: (263) {G5,W8,D3,L2,V3,M1} R(194,3) { ! convergent_lines( X, Z )
% 0.43/1.17 , unequally_directed_lines( parallel_through_point( X, Y ), Z ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 X := parallel_through_point( X, Y )
% 0.43/1.17 Y := Z
% 0.43/1.17 end
% 0.43/1.17 substitution1:
% 0.43/1.17 X := X
% 0.43/1.17 Y := Y
% 0.43/1.17 Z := Z
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 resolution: (642) {G3,W6,D2,L2,V2,M2} { ! convergent_lines( X, Z ), !
% 0.43/1.17 convergent_lines( X, Z ) }.
% 0.43/1.17 parent0[0]: (641) {G2,W9,D3,L2,V3,M2} { ! unequally_directed_lines(
% 0.43/1.17 parallel_through_point( X, Y ), reverse_line( Z ) ), ! convergent_lines(
% 0.43/1.17 X, Z ) }.
% 0.43/1.17 parent1[1]: (262) {G5,W9,D3,L2,V3,M1} R(194,4) { ! convergent_lines( X, Z )
% 0.43/1.17 , unequally_directed_lines( parallel_through_point( X, Y ), reverse_line
% 0.43/1.17 ( Z ) ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 X := X
% 0.43/1.17 Y := Y
% 0.43/1.17 Z := Z
% 0.43/1.17 end
% 0.43/1.17 substitution1:
% 0.43/1.17 X := X
% 0.43/1.17 Y := Y
% 0.43/1.17 Z := Z
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 factor: (643) {G3,W3,D2,L1,V2,M1} { ! convergent_lines( X, Y ) }.
% 0.43/1.17 parent0[0, 1]: (642) {G3,W6,D2,L2,V2,M2} { ! convergent_lines( X, Z ), !
% 0.43/1.17 convergent_lines( X, Z ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 X := X
% 0.43/1.17 Y := Z
% 0.43/1.17 Z := Y
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 subsumption: (362) {G6,W3,D2,L1,V2,M1} R(360,263);r(262) { !
% 0.43/1.17 convergent_lines( X, Z ) }.
% 0.43/1.17 parent0: (643) {G3,W3,D2,L1,V2,M1} { ! convergent_lines( X, Y ) }.
% 0.43/1.17 substitution0:
% 0.43/1.17 X := X
% 0.43/1.17 Y := Z
% 0.43/1.17 end
% 0.43/1.17 permutation0:
% 0.43/1.17 0 ==> 0
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 resolution: (644) {G7,W0,D0,L0,V0,M0} { }.
% 0.43/1.17 parent0[0]: (362) {G6,W3,D2,L1,V2,M1} R(360,263);r(262) { !
% 0.43/1.17 convergent_lines( X, Z ) }.
% 0.43/1.17 parent1[0]: (358) {G8,W7,D4,L1,V2,M1} R(357,354) { convergent_lines(
% 0.43/1.17 parallel_through_point( parallel_through_point( skol1, X ), Y ), skol2 )
% 0.43/1.17 }.
% 0.43/1.17 substitution0:
% 0.43/1.17 X := parallel_through_point( parallel_through_point( skol1, X ), Y )
% 0.43/1.17 Y := Z
% 0.43/1.17 Z := skol2
% 0.43/1.17 end
% 0.43/1.17 substitution1:
% 0.43/1.17 X := X
% 0.43/1.17 Y := Y
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 subsumption: (402) {G9,W0,D0,L0,V0,M0} R(362,358) { }.
% 0.43/1.17 parent0: (644) {G7,W0,D0,L0,V0,M0} { }.
% 0.43/1.17 substitution0:
% 0.43/1.17 end
% 0.43/1.17 permutation0:
% 0.43/1.17 end
% 0.43/1.17
% 0.43/1.17 Proof check complete!
% 0.43/1.17
% 0.43/1.17 Memory use:
% 0.43/1.17
% 0.43/1.17 space for terms: 5757
% 0.43/1.17 space for clauses: 21192
% 0.43/1.17
% 0.43/1.17
% 0.43/1.17 clauses generated: 903
% 0.43/1.17 clauses kept: 403
% 0.43/1.17 clauses selected: 126
% 0.43/1.17 clauses deleted: 22
% 0.43/1.17 clauses inuse deleted: 0
% 0.43/1.17
% 0.43/1.17 subsentry: 3772
% 0.43/1.17 literals s-matched: 2182
% 0.43/1.17 literals matched: 2032
% 0.43/1.17 full subsumption: 599
% 0.43/1.17
% 0.43/1.17 checksum: -449038309
% 0.43/1.17
% 0.43/1.17
% 0.43/1.17 Bliksem ended
%------------------------------------------------------------------------------