%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO234+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n021.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 02:53:07 EDT 2022
% Result : Theorem 0.73s 1.09s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO234+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.03/0.12 % Command : bliksem %s
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Sat Jun 18 06:07:16 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.44/1.08 *** allocated 10000 integers for termspace/termends
% 0.44/1.08 *** allocated 10000 integers for clauses
% 0.44/1.08 *** allocated 10000 integers for justifications
% 0.44/1.08 Bliksem 1.12
% 0.44/1.08
% 0.44/1.08
% 0.44/1.08 Automatic Strategy Selection
% 0.44/1.08
% 0.44/1.08
% 0.44/1.08 Clauses:
% 0.44/1.08
% 0.44/1.08 { ! apart_point_and_line( X, Y ), left_apart_point( X, Y ),
% 0.44/1.08 left_apart_point( X, reverse_line( Y ) ) }.
% 0.44/1.08 { ! left_apart_point( X, Y ), apart_point_and_line( X, Y ) }.
% 0.44/1.08 { ! left_apart_point( X, reverse_line( Y ) ), apart_point_and_line( X, Y )
% 0.44/1.08 }.
% 0.44/1.08 { ! convergent_lines( X, Y ), unequally_directed_lines( X, Y ) }.
% 0.44/1.08 { ! convergent_lines( X, Y ), unequally_directed_lines( X, reverse_line( Y
% 0.44/1.08 ) ) }.
% 0.44/1.08 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.44/1.08 reverse_line( Y ) ), convergent_lines( X, Y ) }.
% 0.44/1.08 { ! divides_points( Z, X, Y ), alpha1( X, Y, Z ), alpha4( X, Y, Z ) }.
% 0.44/1.08 { ! alpha1( X, Y, Z ), divides_points( Z, X, Y ) }.
% 0.44/1.08 { ! alpha4( X, Y, Z ), divides_points( Z, X, Y ) }.
% 0.44/1.08 { ! alpha4( X, Y, Z ), left_apart_point( X, reverse_line( Z ) ) }.
% 0.44/1.08 { ! alpha4( X, Y, Z ), left_apart_point( Y, Z ) }.
% 0.44/1.08 { ! left_apart_point( X, reverse_line( Z ) ), ! left_apart_point( Y, Z ),
% 0.44/1.08 alpha4( X, Y, Z ) }.
% 0.44/1.08 { ! alpha1( X, Y, Z ), left_apart_point( X, Z ) }.
% 0.44/1.08 { ! alpha1( X, Y, Z ), left_apart_point( Y, reverse_line( Z ) ) }.
% 0.44/1.08 { ! left_apart_point( X, Z ), ! left_apart_point( Y, reverse_line( Z ) ),
% 0.44/1.08 alpha1( X, Y, Z ) }.
% 0.44/1.08 { ! before_on_line( X, Y, Z ), distinct_points( Y, Z ) }.
% 0.44/1.08 { ! before_on_line( X, Y, Z ), alpha7( X, Y, Z ) }.
% 0.44/1.08 { ! distinct_points( Y, Z ), ! alpha7( X, Y, Z ), before_on_line( X, Y, Z )
% 0.44/1.08 }.
% 0.44/1.08 { ! alpha7( X, Y, Z ), alpha2( X, Y ) }.
% 0.44/1.08 { ! alpha7( X, Y, Z ), alpha8( X, Y, Z ) }.
% 0.44/1.08 { ! alpha2( X, Y ), ! alpha8( X, Y, Z ), alpha7( X, Y, Z ) }.
% 0.44/1.08 { ! alpha8( X, Y, Z ), alpha5( X, Z ) }.
% 0.44/1.08 { ! alpha8( X, Y, Z ), ! unequally_directed_lines( X, line_connecting( Y, Z
% 0.44/1.08 ) ) }.
% 0.44/1.08 { ! alpha5( X, Z ), unequally_directed_lines( X, line_connecting( Y, Z ) )
% 0.44/1.08 , alpha8( X, Y, Z ) }.
% 0.44/1.08 { ! alpha5( X, Y ), ! left_apart_point( Y, X ) }.
% 0.44/1.08 { ! alpha5( X, Y ), ! left_apart_point( Y, reverse_line( X ) ) }.
% 0.44/1.08 { left_apart_point( Y, X ), left_apart_point( Y, reverse_line( X ) ),
% 0.44/1.08 alpha5( X, Y ) }.
% 0.44/1.08 { ! alpha2( X, Y ), ! left_apart_point( Y, X ) }.
% 0.44/1.08 { ! alpha2( X, Y ), ! left_apart_point( Y, reverse_line( X ) ) }.
% 0.44/1.08 { left_apart_point( Y, X ), left_apart_point( Y, reverse_line( X ) ),
% 0.44/1.08 alpha2( X, Y ) }.
% 0.44/1.08 { ! between_on_line( X, Y, Z, T ), alpha3( X, Y, Z, T ), alpha6( X, Y, Z, T
% 0.44/1.08 ) }.
% 0.44/1.08 { ! alpha3( X, Y, Z, T ), between_on_line( X, Y, Z, T ) }.
% 0.44/1.08 { ! alpha6( X, Y, Z, T ), between_on_line( X, Y, Z, T ) }.
% 0.44/1.08 { ! alpha6( X, Y, Z, T ), before_on_line( X, T, Z ) }.
% 0.44/1.08 { ! alpha6( X, Y, Z, T ), before_on_line( X, Z, Y ) }.
% 0.44/1.08 { ! before_on_line( X, T, Z ), ! before_on_line( X, Z, Y ), alpha6( X, Y, Z
% 0.44/1.08 , T ) }.
% 0.44/1.08 { ! alpha3( X, Y, Z, T ), before_on_line( X, Y, Z ) }.
% 0.44/1.08 { ! alpha3( X, Y, Z, T ), before_on_line( X, Z, T ) }.
% 0.44/1.08 { ! before_on_line( X, Y, Z ), ! before_on_line( X, Z, T ), alpha3( X, Y, Z
% 0.44/1.08 , T ) }.
% 0.44/1.08 { ! distinct_points( X, X ) }.
% 0.44/1.08 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 0.44/1.08 ) }.
% 0.44/1.08 { ! distinct_lines( X, X ) }.
% 0.44/1.08 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.73/1.08 }.
% 0.73/1.08 { ! unequally_directed_lines( X, X ) }.
% 0.73/1.08 { ! unequally_directed_lines( X, Y ), unequally_directed_lines( X, Z ),
% 0.73/1.08 unequally_directed_lines( Y, Z ) }.
% 0.73/1.08 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.73/1.08 reverse_line( Y ) ), alpha9( X, Z ), unequally_directed_lines( Y, Z ) }.
% 0.73/1.08 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.73/1.08 reverse_line( Y ) ), alpha9( X, Z ), unequally_directed_lines( Y,
% 0.73/1.08 reverse_line( Z ) ) }.
% 0.73/1.08 { ! alpha9( X, Y ), unequally_directed_lines( X, Y ) }.
% 0.73/1.08 { ! alpha9( X, Y ), unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.73/1.08 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.73/1.08 reverse_line( Y ) ), alpha9( X, Y ) }.
% 0.73/1.08 { ! line( X ), ! line( Y ), unequally_directed_lines( X, Y ),
% 0.73/1.08 unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.73/1.08 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.73/1.08 reverse_line( Y ) ), left_convergent_lines( X, Y ), left_convergent_lines
% 0.73/1.08 ( X, reverse_line( Y ) ) }.
% 0.73/1.09 { ! left_apart_point( X, Y ) }.
% 0.73/1.09 { ! left_apart_point( X, reverse_line( Y ) ) }.
% 0.73/1.09 { ! left_convergent_lines( X, Y ) }.
% 0.73/1.09 { ! left_convergent_lines( X, reverse_line( Y ) ) }.
% 0.73/1.09 { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line(
% 0.73/1.09 line_connecting( X, Y ) ) }.
% 0.73/1.09 { ! line( X ), ! line( Y ), ! unequally_directed_lines( X, Y ), !
% 0.73/1.09 unequally_directed_lines( X, reverse_line( Y ) ), point(
% 0.73/1.09 intersection_point( X, Y ) ) }.
% 0.73/1.09 { ! point( Y ), ! line( X ), line( parallel_through_point( X, Y ) ) }.
% 0.73/1.09 { ! line( X ), line( reverse_line( X ) ) }.
% 0.73/1.09 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 0.73/1.09 , Y ) ) }.
% 0.73/1.09 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 0.73/1.09 , Y ) ) }.
% 0.73/1.09 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.73/1.09 reverse_line( Y ) ), ! apart_point_and_line( intersection_point( X, Y ),
% 0.73/1.09 X ) }.
% 0.73/1.09 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.73/1.09 reverse_line( Y ) ), ! apart_point_and_line( intersection_point( X, Y ),
% 0.73/1.09 Y ) }.
% 0.73/1.09 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 0.73/1.09 { ! distinct_lines( X, reverse_line( X ) ) }.
% 0.73/1.09 { ! unequally_directed_lines( line_connecting( X, Y ), reverse_line(
% 0.73/1.09 line_connecting( Y, X ) ) ) }.
% 0.73/1.09 { ! unequally_directed_lines( parallel_through_point( Y, X ), Y ) }.
% 0.73/1.09 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), left_apart_point( X
% 0.73/1.09 , Z ), left_apart_point( Y, Z ), left_apart_point( X, T ),
% 0.73/1.09 left_apart_point( Y, T ), left_apart_point( X, reverse_line( Z ) ),
% 0.73/1.09 left_apart_point( Y, reverse_line( Z ) ), left_apart_point( X,
% 0.73/1.09 reverse_line( T ) ), left_apart_point( Y, reverse_line( T ) ) }.
% 0.73/1.09 { ! distinct_points( X, Y ), ! left_apart_point( X, Z ), left_apart_point(
% 0.73/1.09 Y, Z ), left_convergent_lines( line_connecting( X, Y ), Z ) }.
% 0.73/1.09 { ! left_apart_point( X, Y ), distinct_points( X, Z ), left_apart_point( Z
% 0.73/1.09 , Y ) }.
% 0.73/1.09 { ! left_apart_point( X, Y ), ! unequally_directed_lines( Y, Z ),
% 0.73/1.09 distinct_lines( Y, Z ), left_apart_point( X, reverse_line( Z ) ) }.
% 0.73/1.09 { ! left_convergent_lines( X, Y ), unequally_directed_lines( Y, Z ),
% 0.73/1.09 left_convergent_lines( X, Z ) }.
% 0.73/1.09 { unequally_directed_lines( skol1, reverse_line( skol2 ) ) }.
% 0.73/1.09 { ! unequally_directed_lines( skol1, skol3 ) }.
% 0.73/1.09 { ! unequally_directed_lines( skol2, reverse_line( skol3 ) ) }.
% 0.73/1.09
% 0.73/1.09 percentage equality = 0.000000, percentage horn = 0.800000
% 0.73/1.09 This a non-horn, non-equality problem
% 0.73/1.09
% 0.73/1.09
% 0.73/1.09 Options Used:
% 0.73/1.09
% 0.73/1.09 useres = 1
% 0.73/1.09 useparamod = 0
% 0.73/1.09 useeqrefl = 0
% 0.73/1.09 useeqfact = 0
% 0.73/1.09 usefactor = 1
% 0.73/1.09 usesimpsplitting = 0
% 0.73/1.09 usesimpdemod = 0
% 0.73/1.09 usesimpres = 3
% 0.73/1.09
% 0.73/1.09 resimpinuse = 1000
% 0.73/1.09 resimpclauses = 20000
% 0.73/1.09 substype = standard
% 0.73/1.09 backwardsubs = 1
% 0.73/1.09 selectoldest = 5
% 0.73/1.09
% 0.73/1.09 litorderings [0] = split
% 0.73/1.09 litorderings [1] = liftord
% 0.73/1.09
% 0.73/1.09 termordering = none
% 0.73/1.09
% 0.73/1.09 litapriori = 1
% 0.73/1.09 termapriori = 0
% 0.73/1.09 litaposteriori = 0
% 0.73/1.09 termaposteriori = 0
% 0.73/1.09 demodaposteriori = 0
% 0.73/1.09 ordereqreflfact = 0
% 0.73/1.09
% 0.73/1.09 litselect = none
% 0.73/1.09
% 0.73/1.09 maxweight = 15
% 0.73/1.09 maxdepth = 30000
% 0.73/1.09 maxlength = 115
% 0.73/1.09 maxnrvars = 195
% 0.73/1.09 excuselevel = 1
% 0.73/1.09 increasemaxweight = 1
% 0.73/1.09
% 0.73/1.09 maxselected = 10000000
% 0.73/1.09 maxnrclauses = 10000000
% 0.73/1.09
% 0.73/1.09 showgenerated = 0
% 0.73/1.09 showkept = 0
% 0.73/1.09 showselected = 0
% 0.73/1.09 showdeleted = 0
% 0.73/1.09 showresimp = 1
% 0.73/1.09 showstatus = 2000
% 0.73/1.09
% 0.73/1.09 prologoutput = 0
% 0.73/1.09 nrgoals = 5000000
% 0.73/1.09 totalproof = 1
% 0.73/1.09
% 0.73/1.09 Symbols occurring in the translation:
% 0.73/1.09
% 0.73/1.09 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.73/1.09 . [1, 2] (w:1, o:23, a:1, s:1, b:0),
% 0.73/1.09 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 0.73/1.09 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.73/1.09 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.73/1.09 apart_point_and_line [37, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.73/1.09 left_apart_point [38, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.73/1.09 reverse_line [39, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.73/1.09 convergent_lines [41, 2] (w:1, o:49, a:1, s:1, b:0),
% 0.73/1.09 unequally_directed_lines [42, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.73/1.09 divides_points [44, 3] (w:1, o:60, a:1, s:1, b:0),
% 0.73/1.09 before_on_line [45, 3] (w:1, o:65, a:1, s:1, b:0),
% 0.73/1.09 distinct_points [46, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.73/1.09 line_connecting [47, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.73/1.09 between_on_line [49, 4] (w:1, o:68, a:1, s:1, b:0),
% 0.73/1.09 distinct_lines [50, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.73/1.09 line [52, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.73/1.09 left_convergent_lines [53, 2] (w:1, o:54, a:1, s:1, b:0),
% 0.73/1.09 point [54, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.73/1.09 intersection_point [55, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.73/1.09 parallel_through_point [56, 2] (w:1, o:56, a:1, s:1, b:0),
% 0.73/1.09 alpha1 [57, 3] (w:1, o:61, a:1, s:1, b:0),
% 0.73/1.09 alpha2 [58, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.73/1.09 alpha3 [59, 4] (w:1, o:66, a:1, s:1, b:0),
% 0.73/1.09 alpha4 [60, 3] (w:1, o:62, a:1, s:1, b:0),
% 0.73/1.09 alpha5 [61, 2] (w:1, o:58, a:1, s:1, b:0),
% 0.73/1.09 alpha6 [62, 4] (w:1, o:67, a:1, s:1, b:0),
% 0.73/1.09 alpha7 [63, 3] (w:1, o:63, a:1, s:1, b:0),
% 0.73/1.09 alpha8 [64, 3] (w:1, o:64, a:1, s:1, b:0),
% 0.73/1.09 alpha9 [65, 2] (w:1, o:59, a:1, s:1, b:0),
% 0.73/1.09 skol1 [66, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.73/1.09 skol2 [67, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.73/1.09 skol3 [68, 0] (w:1, o:14, a:1, s:1, b:0).
% 0.73/1.09
% 0.73/1.09
% 0.73/1.09 Starting Search:
% 0.73/1.09
% 0.73/1.09 *** allocated 15000 integers for clauses
% 0.73/1.09 *** allocated 22500 integers for clauses
% 0.73/1.09
% 0.73/1.09 Bliksems!, er is een bewijs:
% 0.73/1.09 % SZS status Theorem
% 0.73/1.09 % SZS output start Refutation
% 0.73/1.09
% 0.73/1.09 (43) {G0,W3,D2,L1,V1,M1} I { ! unequally_directed_lines( X, X ) }.
% 0.73/1.09 (44) {G0,W9,D2,L3,V3,M3} I { unequally_directed_lines( X, Z ),
% 0.73/1.09 unequally_directed_lines( Y, Z ), ! unequally_directed_lines( X, Y ) }.
% 0.73/1.09 (51) {G0,W14,D3,L4,V2,M2} I { ! unequally_directed_lines( X, Y ), !
% 0.73/1.09 unequally_directed_lines( X, reverse_line( Y ) ), left_convergent_lines(
% 0.73/1.09 X, reverse_line( Y ) ), left_convergent_lines( X, Y ) }.
% 0.73/1.09 (53) {G0,W3,D2,L1,V2,M1} I { ! left_convergent_lines( X, Y ) }.
% 0.73/1.09 (67) {G0,W4,D3,L1,V0,M1} I { unequally_directed_lines( skol1, reverse_line
% 0.73/1.09 ( skol2 ) ) }.
% 0.73/1.09 (68) {G0,W3,D2,L1,V0,M1} I { ! unequally_directed_lines( skol1, skol3 ) }.
% 0.73/1.09 (69) {G0,W4,D3,L1,V0,M1} I { ! unequally_directed_lines( skol2,
% 0.73/1.09 reverse_line( skol3 ) ) }.
% 0.73/1.09 (119) {G1,W6,D2,L2,V1,M2} R(44,68) { ! unequally_directed_lines( skol1, X )
% 0.73/1.09 , unequally_directed_lines( X, skol3 ) }.
% 0.73/1.09 (121) {G1,W6,D2,L2,V2,M2} R(44,43) { ! unequally_directed_lines( Y, X ),
% 0.73/1.09 unequally_directed_lines( X, Y ) }.
% 0.73/1.09 (135) {G2,W4,D3,L1,V0,M1} R(121,69) { ! unequally_directed_lines(
% 0.73/1.09 reverse_line( skol3 ), skol2 ) }.
% 0.73/1.09 (311) {G1,W7,D3,L2,V2,M2} S(51);r(53);r(53) { ! unequally_directed_lines( X
% 0.73/1.09 , reverse_line( Y ) ), ! unequally_directed_lines( X, Y ) }.
% 0.73/1.09 (343) {G2,W7,D3,L2,V1,M2} R(311,119) { ! unequally_directed_lines( skol1, X
% 0.73/1.09 ), ! unequally_directed_lines( X, reverse_line( skol3 ) ) }.
% 0.73/1.09 (364) {G2,W3,D2,L1,V0,M1} R(311,67) { ! unequally_directed_lines( skol1,
% 0.73/1.09 skol2 ) }.
% 0.73/1.09 (377) {G3,W6,D2,L2,V1,M2} R(364,44) { ! unequally_directed_lines( skol1, X
% 0.73/1.09 ), unequally_directed_lines( X, skol2 ) }.
% 0.73/1.09 (414) {G4,W4,D3,L1,V0,M1} R(377,135) { ! unequally_directed_lines( skol1,
% 0.73/1.09 reverse_line( skol3 ) ) }.
% 0.73/1.09 (425) {G5,W3,D2,L1,V1,M1} R(414,44);r(343) { ! unequally_directed_lines(
% 0.73/1.09 skol1, X ) }.
% 0.73/1.09 (430) {G6,W0,D0,L0,V0,M0} R(425,67) { }.
% 0.73/1.09
% 0.73/1.09
% 0.73/1.09 % SZS output end Refutation
% 0.73/1.09 found a proof!
% 0.73/1.09
% 0.73/1.09 *** allocated 33750 integers for clauses
% 0.73/1.09
% 0.73/1.09 Unprocessed initial clauses:
% 0.73/1.09
% 0.73/1.09 (432) {G0,W10,D3,L3,V2,M3} { ! apart_point_and_line( X, Y ),
% 0.73/1.09 left_apart_point( X, Y ), left_apart_point( X, reverse_line( Y ) ) }.
% 0.73/1.09 (433) {G0,W6,D2,L2,V2,M2} { ! left_apart_point( X, Y ),
% 0.73/1.09 apart_point_and_line( X, Y ) }.
% 0.73/1.09 (434) {G0,W7,D3,L2,V2,M2} { ! left_apart_point( X, reverse_line( Y ) ),
% 0.73/1.09 apart_point_and_line( X, Y ) }.
% 0.73/1.09 (435) {G0,W6,D2,L2,V2,M2} { ! convergent_lines( X, Y ),
% 0.73/1.09 unequally_directed_lines( X, Y ) }.
% 0.73/1.09 (436) {G0,W7,D3,L2,V2,M2} { ! convergent_lines( X, Y ),
% 0.73/1.09 unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.73/1.09 (437) {G0,W10,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y ), !
% 0.73/1.09 unequally_directed_lines( X, reverse_line( Y ) ), convergent_lines( X, Y
% 0.73/1.09 ) }.
% 0.73/1.09 (438) {G0,W12,D2,L3,V3,M3} { ! divides_points( Z, X, Y ), alpha1( X, Y, Z
% 0.73/1.09 ), alpha4( X, Y, Z ) }.
% 0.73/1.09 (439) {G0,W8,D2,L2,V3,M2} { ! alpha1( X, Y, Z ), divides_points( Z, X, Y )
% 0.73/1.09 }.
% 0.73/1.09 (440) {G0,W8,D2,L2,V3,M2} { ! alpha4( X, Y, Z ), divides_points( Z, X, Y )
% 0.73/1.09 }.
% 0.73/1.09 (441) {G0,W8,D3,L2,V3,M2} { ! alpha4( X, Y, Z ), left_apart_point( X,
% 0.73/1.09 reverse_line( Z ) ) }.
% 0.73/1.09 (442) {G0,W7,D2,L2,V3,M2} { ! alpha4( X, Y, Z ), left_apart_point( Y, Z )
% 0.73/1.09 }.
% 0.73/1.09 (443) {G0,W11,D3,L3,V3,M3} { ! left_apart_point( X, reverse_line( Z ) ), !
% 0.73/1.09 left_apart_point( Y, Z ), alpha4( X, Y, Z ) }.
% 0.73/1.09 (444) {G0,W7,D2,L2,V3,M2} { ! alpha1( X, Y, Z ), left_apart_point( X, Z )
% 0.73/1.09 }.
% 0.73/1.09 (445) {G0,W8,D3,L2,V3,M2} { ! alpha1( X, Y, Z ), left_apart_point( Y,
% 0.73/1.09 reverse_line( Z ) ) }.
% 0.73/1.09 (446) {G0,W11,D3,L3,V3,M3} { ! left_apart_point( X, Z ), !
% 0.73/1.09 left_apart_point( Y, reverse_line( Z ) ), alpha1( X, Y, Z ) }.
% 0.73/1.09 (447) {G0,W7,D2,L2,V3,M2} { ! before_on_line( X, Y, Z ), distinct_points(
% 0.73/1.09 Y, Z ) }.
% 0.73/1.09 (448) {G0,W8,D2,L2,V3,M2} { ! before_on_line( X, Y, Z ), alpha7( X, Y, Z )
% 0.73/1.09 }.
% 0.73/1.09 (449) {G0,W11,D2,L3,V3,M3} { ! distinct_points( Y, Z ), ! alpha7( X, Y, Z
% 0.73/1.09 ), before_on_line( X, Y, Z ) }.
% 0.73/1.09 (450) {G0,W7,D2,L2,V3,M2} { ! alpha7( X, Y, Z ), alpha2( X, Y ) }.
% 0.73/1.09 (451) {G0,W8,D2,L2,V3,M2} { ! alpha7( X, Y, Z ), alpha8( X, Y, Z ) }.
% 0.73/1.09 (452) {G0,W11,D2,L3,V3,M3} { ! alpha2( X, Y ), ! alpha8( X, Y, Z ), alpha7
% 0.73/1.09 ( X, Y, Z ) }.
% 0.73/1.09 (453) {G0,W7,D2,L2,V3,M2} { ! alpha8( X, Y, Z ), alpha5( X, Z ) }.
% 0.73/1.09 (454) {G0,W9,D3,L2,V3,M2} { ! alpha8( X, Y, Z ), !
% 0.73/1.09 unequally_directed_lines( X, line_connecting( Y, Z ) ) }.
% 0.73/1.09 (455) {G0,W12,D3,L3,V3,M3} { ! alpha5( X, Z ), unequally_directed_lines( X
% 0.73/1.09 , line_connecting( Y, Z ) ), alpha8( X, Y, Z ) }.
% 0.73/1.09 (456) {G0,W6,D2,L2,V2,M2} { ! alpha5( X, Y ), ! left_apart_point( Y, X )
% 0.73/1.09 }.
% 0.73/1.09 (457) {G0,W7,D3,L2,V2,M2} { ! alpha5( X, Y ), ! left_apart_point( Y,
% 0.73/1.09 reverse_line( X ) ) }.
% 0.73/1.09 (458) {G0,W10,D3,L3,V2,M3} { left_apart_point( Y, X ), left_apart_point( Y
% 0.73/1.09 , reverse_line( X ) ), alpha5( X, Y ) }.
% 0.73/1.09 (459) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), ! left_apart_point( Y, X )
% 0.73/1.09 }.
% 0.73/1.09 (460) {G0,W7,D3,L2,V2,M2} { ! alpha2( X, Y ), ! left_apart_point( Y,
% 0.73/1.09 reverse_line( X ) ) }.
% 0.73/1.09 (461) {G0,W10,D3,L3,V2,M3} { left_apart_point( Y, X ), left_apart_point( Y
% 0.73/1.09 , reverse_line( X ) ), alpha2( X, Y ) }.
% 0.73/1.09 (462) {G0,W15,D2,L3,V4,M3} { ! between_on_line( X, Y, Z, T ), alpha3( X, Y
% 0.73/1.09 , Z, T ), alpha6( X, Y, Z, T ) }.
% 0.73/1.09 (463) {G0,W10,D2,L2,V4,M2} { ! alpha3( X, Y, Z, T ), between_on_line( X, Y
% 0.73/1.09 , Z, T ) }.
% 0.73/1.09 (464) {G0,W10,D2,L2,V4,M2} { ! alpha6( X, Y, Z, T ), between_on_line( X, Y
% 0.73/1.09 , Z, T ) }.
% 0.73/1.09 (465) {G0,W9,D2,L2,V4,M2} { ! alpha6( X, Y, Z, T ), before_on_line( X, T,
% 0.73/1.09 Z ) }.
% 0.73/1.09 (466) {G0,W9,D2,L2,V4,M2} { ! alpha6( X, Y, Z, T ), before_on_line( X, Z,
% 0.73/1.09 Y ) }.
% 0.73/1.09 (467) {G0,W13,D2,L3,V4,M3} { ! before_on_line( X, T, Z ), ! before_on_line
% 0.73/1.09 ( X, Z, Y ), alpha6( X, Y, Z, T ) }.
% 0.73/1.09 (468) {G0,W9,D2,L2,V4,M2} { ! alpha3( X, Y, Z, T ), before_on_line( X, Y,
% 0.73/1.09 Z ) }.
% 0.73/1.09 (469) {G0,W9,D2,L2,V4,M2} { ! alpha3( X, Y, Z, T ), before_on_line( X, Z,
% 0.73/1.09 T ) }.
% 0.73/1.09 (470) {G0,W13,D2,L3,V4,M3} { ! before_on_line( X, Y, Z ), ! before_on_line
% 0.73/1.09 ( X, Z, T ), alpha3( X, Y, Z, T ) }.
% 0.73/1.09 (471) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 0.73/1.09 (472) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 0.73/1.09 , Z ), distinct_points( Y, Z ) }.
% 0.73/1.09 (473) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.73/1.09 (474) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X, Z
% 0.73/1.09 ), distinct_lines( Y, Z ) }.
% 0.73/1.09 (475) {G0,W3,D2,L1,V1,M1} { ! unequally_directed_lines( X, X ) }.
% 0.73/1.09 (476) {G0,W9,D2,L3,V3,M3} { ! unequally_directed_lines( X, Y ),
% 0.73/1.09 unequally_directed_lines( X, Z ), unequally_directed_lines( Y, Z ) }.
% 0.73/1.09 (477) {G0,W13,D3,L4,V3,M4} { ! unequally_directed_lines( X, Y ), !
% 0.73/1.09 unequally_directed_lines( X, reverse_line( Y ) ), alpha9( X, Z ),
% 0.73/1.09 unequally_directed_lines( Y, Z ) }.
% 0.73/1.09 (478) {G0,W14,D3,L4,V3,M4} { ! unequally_directed_lines( X, Y ), !
% 0.73/1.09 unequally_directed_lines( X, reverse_line( Y ) ), alpha9( X, Z ),
% 0.73/1.09 unequally_directed_lines( Y, reverse_line( Z ) ) }.
% 0.73/1.09 (479) {G0,W6,D2,L2,V2,M2} { ! alpha9( X, Y ), unequally_directed_lines( X
% 0.73/1.09 , Y ) }.
% 0.73/1.09 (480) {G0,W7,D3,L2,V2,M2} { ! alpha9( X, Y ), unequally_directed_lines( X
% 0.73/1.09 , reverse_line( Y ) ) }.
% 0.73/1.09 (481) {G0,W10,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y ), !
% 0.73/1.09 unequally_directed_lines( X, reverse_line( Y ) ), alpha9( X, Y ) }.
% 0.73/1.09 (482) {G0,W11,D3,L4,V2,M4} { ! line( X ), ! line( Y ),
% 0.73/1.09 unequally_directed_lines( X, Y ), unequally_directed_lines( X,
% 0.73/1.09 reverse_line( Y ) ) }.
% 0.73/1.09 (483) {G0,W14,D3,L4,V2,M4} { ! unequally_directed_lines( X, Y ), !
% 0.73/1.09 unequally_directed_lines( X, reverse_line( Y ) ), left_convergent_lines(
% 0.73/1.09 X, Y ), left_convergent_lines( X, reverse_line( Y ) ) }.
% 0.73/1.09 (484) {G0,W3,D2,L1,V2,M1} { ! left_apart_point( X, Y ) }.
% 0.73/1.09 (485) {G0,W4,D3,L1,V2,M1} { ! left_apart_point( X, reverse_line( Y ) ) }.
% 0.73/1.09 (486) {G0,W3,D2,L1,V2,M1} { ! left_convergent_lines( X, Y ) }.
% 0.73/1.09 (487) {G0,W4,D3,L1,V2,M1} { ! left_convergent_lines( X, reverse_line( Y )
% 0.73/1.09 ) }.
% 0.73/1.09 (488) {G0,W11,D3,L4,V2,M4} { ! point( X ), ! point( Y ), ! distinct_points
% 0.73/1.09 ( X, Y ), line( line_connecting( X, Y ) ) }.
% 0.73/1.09 (489) {G0,W15,D3,L5,V2,M5} { ! line( X ), ! line( Y ), !
% 0.73/1.09 unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.73/1.09 reverse_line( Y ) ), point( intersection_point( X, Y ) ) }.
% 0.73/1.09 (490) {G0,W8,D3,L3,V2,M3} { ! point( Y ), ! line( X ), line(
% 0.73/1.09 parallel_through_point( X, Y ) ) }.
% 0.73/1.09 (491) {G0,W5,D3,L2,V1,M2} { ! line( X ), line( reverse_line( X ) ) }.
% 0.73/1.09 (492) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.73/1.09 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 0.73/1.09 (493) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.73/1.09 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 0.73/1.09 (494) {G0,W12,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y ), !
% 0.73/1.09 unequally_directed_lines( X, reverse_line( Y ) ), ! apart_point_and_line
% 0.73/1.09 ( intersection_point( X, Y ), X ) }.
% 0.73/1.09 (495) {G0,W12,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y ), !
% 0.73/1.09 unequally_directed_lines( X, reverse_line( Y ) ), ! apart_point_and_line
% 0.73/1.09 ( intersection_point( X, Y ), Y ) }.
% 0.73/1.09 (496) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.73/1.09 parallel_through_point( Y, X ) ) }.
% 0.73/1.09 (497) {G0,W4,D3,L1,V1,M1} { ! distinct_lines( X, reverse_line( X ) ) }.
% 0.73/1.09 (498) {G0,W8,D4,L1,V2,M1} { ! unequally_directed_lines( line_connecting( X
% 0.73/1.09 , Y ), reverse_line( line_connecting( Y, X ) ) ) }.
% 0.73/1.09 (499) {G0,W5,D3,L1,V2,M1} { ! unequally_directed_lines(
% 0.73/1.09 parallel_through_point( Y, X ), Y ) }.
% 0.73/1.09 (500) {G0,W34,D3,L10,V4,M10} { ! distinct_points( X, Y ), ! distinct_lines
% 0.73/1.09 ( Z, T ), left_apart_point( X, Z ), left_apart_point( Y, Z ),
% 0.73/1.09 left_apart_point( X, T ), left_apart_point( Y, T ), left_apart_point( X,
% 0.73/1.09 reverse_line( Z ) ), left_apart_point( Y, reverse_line( Z ) ),
% 0.73/1.09 left_apart_point( X, reverse_line( T ) ), left_apart_point( Y,
% 0.73/1.09 reverse_line( T ) ) }.
% 0.73/1.09 (501) {G0,W14,D3,L4,V3,M4} { ! distinct_points( X, Y ), ! left_apart_point
% 0.73/1.09 ( X, Z ), left_apart_point( Y, Z ), left_convergent_lines(
% 0.73/1.09 line_connecting( X, Y ), Z ) }.
% 0.73/1.09 (502) {G0,W9,D2,L3,V3,M3} { ! left_apart_point( X, Y ), distinct_points( X
% 0.73/1.09 , Z ), left_apart_point( Z, Y ) }.
% 0.73/1.09 (503) {G0,W13,D3,L4,V3,M4} { ! left_apart_point( X, Y ), !
% 0.73/1.09 unequally_directed_lines( Y, Z ), distinct_lines( Y, Z ),
% 0.73/1.09 left_apart_point( X, reverse_line( Z ) ) }.
% 0.73/1.09 (504) {G0,W9,D2,L3,V3,M3} { ! left_convergent_lines( X, Y ),
% 0.73/1.09 unequally_directed_lines( Y, Z ), left_convergent_lines( X, Z ) }.
% 0.73/1.09 (505) {G0,W4,D3,L1,V0,M1} { unequally_directed_lines( skol1, reverse_line
% 0.73/1.09 ( skol2 ) ) }.
% 0.73/1.09 (506) {G0,W3,D2,L1,V0,M1} { ! unequally_directed_lines( skol1, skol3 ) }.
% 0.73/1.09 (507) {G0,W4,D3,L1,V0,M1} { ! unequally_directed_lines( skol2,
% 0.73/1.09 reverse_line( skol3 ) ) }.
% 0.73/1.09
% 0.73/1.09
% 0.73/1.09 Total Proof:
% 0.73/1.09
% 0.73/1.09 subsumption: (43) {G0,W3,D2,L1,V1,M1} I { ! unequally_directed_lines( X, X
% 0.73/1.09 ) }.
% 0.73/1.09 parent0: (475) {G0,W3,D2,L1,V1,M1} { ! unequally_directed_lines( X, X )
% 0.73/1.09 }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 end
% 0.73/1.09 permutation0:
% 0.73/1.09 0 ==> 0
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 subsumption: (44) {G0,W9,D2,L3,V3,M3} I { unequally_directed_lines( X, Z )
% 0.73/1.09 , unequally_directed_lines( Y, Z ), ! unequally_directed_lines( X, Y )
% 0.73/1.09 }.
% 0.73/1.09 parent0: (476) {G0,W9,D2,L3,V3,M3} { ! unequally_directed_lines( X, Y ),
% 0.73/1.09 unequally_directed_lines( X, Z ), unequally_directed_lines( Y, Z ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 Y := Y
% 0.73/1.09 Z := Z
% 0.73/1.09 end
% 0.73/1.09 permutation0:
% 0.73/1.09 0 ==> 2
% 0.73/1.09 1 ==> 0
% 0.73/1.09 2 ==> 1
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 subsumption: (51) {G0,W14,D3,L4,V2,M2} I { ! unequally_directed_lines( X, Y
% 0.73/1.09 ), ! unequally_directed_lines( X, reverse_line( Y ) ),
% 0.73/1.09 left_convergent_lines( X, reverse_line( Y ) ), left_convergent_lines( X,
% 0.73/1.09 Y ) }.
% 0.73/1.09 parent0: (483) {G0,W14,D3,L4,V2,M4} { ! unequally_directed_lines( X, Y ),
% 0.73/1.09 ! unequally_directed_lines( X, reverse_line( Y ) ), left_convergent_lines
% 0.73/1.09 ( X, Y ), left_convergent_lines( X, reverse_line( Y ) ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 Y := Y
% 0.73/1.09 end
% 0.73/1.09 permutation0:
% 0.73/1.09 0 ==> 0
% 0.73/1.09 1 ==> 1
% 0.73/1.09 2 ==> 3
% 0.73/1.09 3 ==> 2
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 subsumption: (53) {G0,W3,D2,L1,V2,M1} I { ! left_convergent_lines( X, Y )
% 0.73/1.09 }.
% 0.73/1.09 parent0: (486) {G0,W3,D2,L1,V2,M1} { ! left_convergent_lines( X, Y ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 Y := Y
% 0.73/1.09 end
% 0.73/1.09 permutation0:
% 0.73/1.09 0 ==> 0
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 subsumption: (67) {G0,W4,D3,L1,V0,M1} I { unequally_directed_lines( skol1,
% 0.73/1.09 reverse_line( skol2 ) ) }.
% 0.73/1.09 parent0: (505) {G0,W4,D3,L1,V0,M1} { unequally_directed_lines( skol1,
% 0.73/1.09 reverse_line( skol2 ) ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 end
% 0.73/1.09 permutation0:
% 0.73/1.09 0 ==> 0
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 subsumption: (68) {G0,W3,D2,L1,V0,M1} I { ! unequally_directed_lines( skol1
% 0.73/1.09 , skol3 ) }.
% 0.73/1.09 parent0: (506) {G0,W3,D2,L1,V0,M1} { ! unequally_directed_lines( skol1,
% 0.73/1.09 skol3 ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 end
% 0.73/1.09 permutation0:
% 0.73/1.09 0 ==> 0
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 subsumption: (69) {G0,W4,D3,L1,V0,M1} I { ! unequally_directed_lines( skol2
% 0.73/1.09 , reverse_line( skol3 ) ) }.
% 0.73/1.09 parent0: (507) {G0,W4,D3,L1,V0,M1} { ! unequally_directed_lines( skol2,
% 0.73/1.09 reverse_line( skol3 ) ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 end
% 0.73/1.09 permutation0:
% 0.73/1.09 0 ==> 0
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 resolution: (631) {G1,W6,D2,L2,V1,M2} { unequally_directed_lines( X, skol3
% 0.73/1.09 ), ! unequally_directed_lines( skol1, X ) }.
% 0.73/1.09 parent0[0]: (68) {G0,W3,D2,L1,V0,M1} I { ! unequally_directed_lines( skol1
% 0.73/1.09 , skol3 ) }.
% 0.73/1.09 parent1[0]: (44) {G0,W9,D2,L3,V3,M3} I { unequally_directed_lines( X, Z ),
% 0.73/1.09 unequally_directed_lines( Y, Z ), ! unequally_directed_lines( X, Y ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 end
% 0.73/1.09 substitution1:
% 0.73/1.09 X := skol1
% 0.73/1.09 Y := X
% 0.73/1.09 Z := skol3
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 subsumption: (119) {G1,W6,D2,L2,V1,M2} R(44,68) { !
% 0.73/1.09 unequally_directed_lines( skol1, X ), unequally_directed_lines( X, skol3
% 0.73/1.09 ) }.
% 0.73/1.09 parent0: (631) {G1,W6,D2,L2,V1,M2} { unequally_directed_lines( X, skol3 )
% 0.73/1.09 , ! unequally_directed_lines( skol1, X ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 end
% 0.73/1.09 permutation0:
% 0.73/1.09 0 ==> 1
% 0.73/1.09 1 ==> 0
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 resolution: (633) {G1,W6,D2,L2,V2,M2} { unequally_directed_lines( Y, X ),
% 0.73/1.09 ! unequally_directed_lines( X, Y ) }.
% 0.73/1.09 parent0[0]: (43) {G0,W3,D2,L1,V1,M1} I { ! unequally_directed_lines( X, X )
% 0.73/1.09 }.
% 0.73/1.09 parent1[0]: (44) {G0,W9,D2,L3,V3,M3} I { unequally_directed_lines( X, Z ),
% 0.73/1.09 unequally_directed_lines( Y, Z ), ! unequally_directed_lines( X, Y ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 end
% 0.73/1.09 substitution1:
% 0.73/1.09 X := X
% 0.73/1.09 Y := Y
% 0.73/1.09 Z := X
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 subsumption: (121) {G1,W6,D2,L2,V2,M2} R(44,43) { !
% 0.73/1.09 unequally_directed_lines( Y, X ), unequally_directed_lines( X, Y ) }.
% 0.73/1.09 parent0: (633) {G1,W6,D2,L2,V2,M2} { unequally_directed_lines( Y, X ), !
% 0.73/1.09 unequally_directed_lines( X, Y ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := Y
% 0.73/1.09 Y := X
% 0.73/1.09 end
% 0.73/1.09 permutation0:
% 0.73/1.09 0 ==> 1
% 0.73/1.09 1 ==> 0
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 resolution: (635) {G1,W4,D3,L1,V0,M1} { ! unequally_directed_lines(
% 0.73/1.09 reverse_line( skol3 ), skol2 ) }.
% 0.73/1.09 parent0[0]: (69) {G0,W4,D3,L1,V0,M1} I { ! unequally_directed_lines( skol2
% 0.73/1.09 , reverse_line( skol3 ) ) }.
% 0.73/1.09 parent1[1]: (121) {G1,W6,D2,L2,V2,M2} R(44,43) { ! unequally_directed_lines
% 0.73/1.09 ( Y, X ), unequally_directed_lines( X, Y ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 end
% 0.73/1.09 substitution1:
% 0.73/1.09 X := skol2
% 0.73/1.09 Y := reverse_line( skol3 )
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 subsumption: (135) {G2,W4,D3,L1,V0,M1} R(121,69) { !
% 0.73/1.09 unequally_directed_lines( reverse_line( skol3 ), skol2 ) }.
% 0.73/1.09 parent0: (635) {G1,W4,D3,L1,V0,M1} { ! unequally_directed_lines(
% 0.73/1.09 reverse_line( skol3 ), skol2 ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 end
% 0.73/1.09 permutation0:
% 0.73/1.09 0 ==> 0
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 resolution: (636) {G1,W10,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y
% 0.73/1.09 ), ! unequally_directed_lines( X, reverse_line( Y ) ),
% 0.73/1.09 left_convergent_lines( X, Y ) }.
% 0.73/1.09 parent0[0]: (53) {G0,W3,D2,L1,V2,M1} I { ! left_convergent_lines( X, Y )
% 0.73/1.09 }.
% 0.73/1.09 parent1[2]: (51) {G0,W14,D3,L4,V2,M2} I { ! unequally_directed_lines( X, Y
% 0.73/1.09 ), ! unequally_directed_lines( X, reverse_line( Y ) ),
% 0.73/1.09 left_convergent_lines( X, reverse_line( Y ) ), left_convergent_lines( X,
% 0.73/1.09 Y ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 Y := reverse_line( Y )
% 0.73/1.09 end
% 0.73/1.09 substitution1:
% 0.73/1.09 X := X
% 0.73/1.09 Y := Y
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 resolution: (638) {G1,W7,D3,L2,V2,M2} { ! unequally_directed_lines( X, Y )
% 0.73/1.09 , ! unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.73/1.09 parent0[0]: (53) {G0,W3,D2,L1,V2,M1} I { ! left_convergent_lines( X, Y )
% 0.73/1.09 }.
% 0.73/1.09 parent1[2]: (636) {G1,W10,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y
% 0.73/1.09 ), ! unequally_directed_lines( X, reverse_line( Y ) ),
% 0.73/1.09 left_convergent_lines( X, Y ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 Y := Y
% 0.73/1.09 end
% 0.73/1.09 substitution1:
% 0.73/1.09 X := X
% 0.73/1.09 Y := Y
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 subsumption: (311) {G1,W7,D3,L2,V2,M2} S(51);r(53);r(53) { !
% 0.73/1.09 unequally_directed_lines( X, reverse_line( Y ) ), !
% 0.73/1.09 unequally_directed_lines( X, Y ) }.
% 0.73/1.09 parent0: (638) {G1,W7,D3,L2,V2,M2} { ! unequally_directed_lines( X, Y ), !
% 0.73/1.09 unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 Y := Y
% 0.73/1.09 end
% 0.73/1.09 permutation0:
% 0.73/1.09 0 ==> 1
% 0.73/1.09 1 ==> 0
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 resolution: (639) {G2,W7,D3,L2,V1,M2} { ! unequally_directed_lines( X,
% 0.73/1.09 reverse_line( skol3 ) ), ! unequally_directed_lines( skol1, X ) }.
% 0.73/1.09 parent0[1]: (311) {G1,W7,D3,L2,V2,M2} S(51);r(53);r(53) { !
% 0.73/1.09 unequally_directed_lines( X, reverse_line( Y ) ), !
% 0.73/1.09 unequally_directed_lines( X, Y ) }.
% 0.73/1.09 parent1[1]: (119) {G1,W6,D2,L2,V1,M2} R(44,68) { ! unequally_directed_lines
% 0.73/1.09 ( skol1, X ), unequally_directed_lines( X, skol3 ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 Y := skol3
% 0.73/1.09 end
% 0.73/1.09 substitution1:
% 0.73/1.09 X := X
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 subsumption: (343) {G2,W7,D3,L2,V1,M2} R(311,119) { !
% 0.73/1.09 unequally_directed_lines( skol1, X ), ! unequally_directed_lines( X,
% 0.73/1.09 reverse_line( skol3 ) ) }.
% 0.73/1.09 parent0: (639) {G2,W7,D3,L2,V1,M2} { ! unequally_directed_lines( X,
% 0.73/1.09 reverse_line( skol3 ) ), ! unequally_directed_lines( skol1, X ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 end
% 0.73/1.09 permutation0:
% 0.73/1.09 0 ==> 1
% 0.73/1.09 1 ==> 0
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 resolution: (640) {G1,W3,D2,L1,V0,M1} { ! unequally_directed_lines( skol1
% 0.73/1.09 , skol2 ) }.
% 0.73/1.09 parent0[0]: (311) {G1,W7,D3,L2,V2,M2} S(51);r(53);r(53) { !
% 0.73/1.09 unequally_directed_lines( X, reverse_line( Y ) ), !
% 0.73/1.09 unequally_directed_lines( X, Y ) }.
% 0.73/1.09 parent1[0]: (67) {G0,W4,D3,L1,V0,M1} I { unequally_directed_lines( skol1,
% 0.73/1.09 reverse_line( skol2 ) ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := skol1
% 0.73/1.09 Y := skol2
% 0.73/1.09 end
% 0.73/1.09 substitution1:
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 subsumption: (364) {G2,W3,D2,L1,V0,M1} R(311,67) { !
% 0.73/1.09 unequally_directed_lines( skol1, skol2 ) }.
% 0.73/1.09 parent0: (640) {G1,W3,D2,L1,V0,M1} { ! unequally_directed_lines( skol1,
% 0.73/1.09 skol2 ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 end
% 0.73/1.09 permutation0:
% 0.73/1.09 0 ==> 0
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 resolution: (642) {G1,W6,D2,L2,V1,M2} { unequally_directed_lines( X, skol2
% 0.73/1.09 ), ! unequally_directed_lines( skol1, X ) }.
% 0.73/1.09 parent0[0]: (364) {G2,W3,D2,L1,V0,M1} R(311,67) { !
% 0.73/1.09 unequally_directed_lines( skol1, skol2 ) }.
% 0.73/1.09 parent1[0]: (44) {G0,W9,D2,L3,V3,M3} I { unequally_directed_lines( X, Z ),
% 0.73/1.09 unequally_directed_lines( Y, Z ), ! unequally_directed_lines( X, Y ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 end
% 0.73/1.09 substitution1:
% 0.73/1.09 X := skol1
% 0.73/1.09 Y := X
% 0.73/1.09 Z := skol2
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 subsumption: (377) {G3,W6,D2,L2,V1,M2} R(364,44) { !
% 0.73/1.09 unequally_directed_lines( skol1, X ), unequally_directed_lines( X, skol2
% 0.73/1.09 ) }.
% 0.73/1.09 parent0: (642) {G1,W6,D2,L2,V1,M2} { unequally_directed_lines( X, skol2 )
% 0.73/1.09 , ! unequally_directed_lines( skol1, X ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 end
% 0.73/1.09 permutation0:
% 0.73/1.09 0 ==> 1
% 0.73/1.09 1 ==> 0
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 resolution: (644) {G3,W4,D3,L1,V0,M1} { ! unequally_directed_lines( skol1
% 0.73/1.09 , reverse_line( skol3 ) ) }.
% 0.73/1.09 parent0[0]: (135) {G2,W4,D3,L1,V0,M1} R(121,69) { !
% 0.73/1.09 unequally_directed_lines( reverse_line( skol3 ), skol2 ) }.
% 0.73/1.09 parent1[1]: (377) {G3,W6,D2,L2,V1,M2} R(364,44) { !
% 0.73/1.09 unequally_directed_lines( skol1, X ), unequally_directed_lines( X, skol2
% 0.73/1.09 ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 end
% 0.73/1.09 substitution1:
% 0.73/1.09 X := reverse_line( skol3 )
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 subsumption: (414) {G4,W4,D3,L1,V0,M1} R(377,135) { !
% 0.73/1.09 unequally_directed_lines( skol1, reverse_line( skol3 ) ) }.
% 0.73/1.09 parent0: (644) {G3,W4,D3,L1,V0,M1} { ! unequally_directed_lines( skol1,
% 0.73/1.09 reverse_line( skol3 ) ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 end
% 0.73/1.09 permutation0:
% 0.73/1.09 0 ==> 0
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 resolution: (645) {G1,W7,D3,L2,V1,M2} { unequally_directed_lines( X,
% 0.73/1.09 reverse_line( skol3 ) ), ! unequally_directed_lines( skol1, X ) }.
% 0.73/1.09 parent0[0]: (414) {G4,W4,D3,L1,V0,M1} R(377,135) { !
% 0.73/1.09 unequally_directed_lines( skol1, reverse_line( skol3 ) ) }.
% 0.73/1.09 parent1[0]: (44) {G0,W9,D2,L3,V3,M3} I { unequally_directed_lines( X, Z ),
% 0.73/1.09 unequally_directed_lines( Y, Z ), ! unequally_directed_lines( X, Y ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 end
% 0.73/1.09 substitution1:
% 0.73/1.09 X := skol1
% 0.73/1.09 Y := X
% 0.73/1.09 Z := reverse_line( skol3 )
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 resolution: (647) {G2,W6,D2,L2,V1,M2} { ! unequally_directed_lines( skol1
% 0.73/1.09 , X ), ! unequally_directed_lines( skol1, X ) }.
% 0.73/1.09 parent0[1]: (343) {G2,W7,D3,L2,V1,M2} R(311,119) { !
% 0.73/1.09 unequally_directed_lines( skol1, X ), ! unequally_directed_lines( X,
% 0.73/1.09 reverse_line( skol3 ) ) }.
% 0.73/1.09 parent1[0]: (645) {G1,W7,D3,L2,V1,M2} { unequally_directed_lines( X,
% 0.73/1.09 reverse_line( skol3 ) ), ! unequally_directed_lines( skol1, X ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 end
% 0.73/1.09 substitution1:
% 0.73/1.09 X := X
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 factor: (648) {G2,W3,D2,L1,V1,M1} { ! unequally_directed_lines( skol1, X )
% 0.73/1.09 }.
% 0.73/1.09 parent0[0, 1]: (647) {G2,W6,D2,L2,V1,M2} { ! unequally_directed_lines(
% 0.73/1.09 skol1, X ), ! unequally_directed_lines( skol1, X ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 subsumption: (425) {G5,W3,D2,L1,V1,M1} R(414,44);r(343) { !
% 0.73/1.09 unequally_directed_lines( skol1, X ) }.
% 0.73/1.09 parent0: (648) {G2,W3,D2,L1,V1,M1} { ! unequally_directed_lines( skol1, X
% 0.73/1.09 ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := X
% 0.73/1.09 end
% 0.73/1.09 permutation0:
% 0.73/1.09 0 ==> 0
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 resolution: (649) {G1,W0,D0,L0,V0,M0} { }.
% 0.73/1.09 parent0[0]: (425) {G5,W3,D2,L1,V1,M1} R(414,44);r(343) { !
% 0.73/1.09 unequally_directed_lines( skol1, X ) }.
% 0.73/1.09 parent1[0]: (67) {G0,W4,D3,L1,V0,M1} I { unequally_directed_lines( skol1,
% 0.73/1.09 reverse_line( skol2 ) ) }.
% 0.73/1.09 substitution0:
% 0.73/1.09 X := reverse_line( skol2 )
% 0.73/1.09 end
% 0.73/1.09 substitution1:
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 subsumption: (430) {G6,W0,D0,L0,V0,M0} R(425,67) { }.
% 0.73/1.09 parent0: (649) {G1,W0,D0,L0,V0,M0} { }.
% 0.73/1.09 substitution0:
% 0.73/1.09 end
% 0.73/1.09 permutation0:
% 0.73/1.09 end
% 0.73/1.09
% 0.73/1.09 Proof check complete!
% 0.73/1.09
% 0.73/1.09 Memory use:
% 0.73/1.09
% 0.73/1.09 space for terms: 5895
% 0.73/1.09 space for clauses: 21258
% 0.73/1.09
% 0.73/1.09
% 0.73/1.09 clauses generated: 1013
% 0.73/1.09 clauses kept: 431
% 0.73/1.09 clauses selected: 151
% 0.73/1.09 clauses deleted: 27
% 0.73/1.09 clauses inuse deleted: 0
% 0.73/1.09
% 0.73/1.09 subsentry: 3165
% 0.73/1.09 literals s-matched: 1936
% 0.73/1.09 literals matched: 1786
% 0.73/1.09 full subsumption: 546
% 0.73/1.09
% 0.73/1.09 checksum: 968198257
% 0.73/1.09
% 0.73/1.09
% 0.73/1.09 Bliksem ended
%------------------------------------------------------------------------------