TSTP Solution File: GEO254+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO254+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 02:53:18 EDT 2022
% Result : Theorem 0.73s 1.10s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GEO254+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.03/0.12 % 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 14:40:29 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.42/1.06 *** allocated 10000 integers for termspace/termends
% 0.42/1.06 *** allocated 10000 integers for clauses
% 0.42/1.06 *** allocated 10000 integers for justifications
% 0.42/1.06 Bliksem 1.12
% 0.42/1.06
% 0.42/1.06
% 0.42/1.06 Automatic Strategy Selection
% 0.42/1.06
% 0.42/1.06
% 0.42/1.06 Clauses:
% 0.42/1.06
% 0.42/1.06 { ! apart_point_and_line( X, Y ), left_apart_point( X, Y ),
% 0.42/1.06 left_apart_point( X, reverse_line( Y ) ) }.
% 0.42/1.06 { ! left_apart_point( X, Y ), apart_point_and_line( X, Y ) }.
% 0.42/1.06 { ! left_apart_point( X, reverse_line( Y ) ), apart_point_and_line( X, Y )
% 0.42/1.06 }.
% 0.42/1.06 { ! convergent_lines( X, Y ), unequally_directed_lines( X, Y ) }.
% 0.42/1.06 { ! convergent_lines( X, Y ), unequally_directed_lines( X, reverse_line( Y
% 0.42/1.06 ) ) }.
% 0.42/1.06 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.42/1.06 reverse_line( Y ) ), convergent_lines( X, Y ) }.
% 0.42/1.06 { ! divides_points( Z, X, Y ), alpha1( X, Y, Z ), alpha4( X, Y, Z ) }.
% 0.42/1.06 { ! alpha1( X, Y, Z ), divides_points( Z, X, Y ) }.
% 0.42/1.06 { ! alpha4( X, Y, Z ), divides_points( Z, X, Y ) }.
% 0.42/1.06 { ! alpha4( X, Y, Z ), left_apart_point( X, reverse_line( Z ) ) }.
% 0.42/1.06 { ! alpha4( X, Y, Z ), left_apart_point( Y, Z ) }.
% 0.42/1.06 { ! left_apart_point( X, reverse_line( Z ) ), ! left_apart_point( Y, Z ),
% 0.42/1.06 alpha4( X, Y, Z ) }.
% 0.42/1.06 { ! alpha1( X, Y, Z ), left_apart_point( X, Z ) }.
% 0.42/1.06 { ! alpha1( X, Y, Z ), left_apart_point( Y, reverse_line( Z ) ) }.
% 0.42/1.06 { ! left_apart_point( X, Z ), ! left_apart_point( Y, reverse_line( Z ) ),
% 0.42/1.06 alpha1( X, Y, Z ) }.
% 0.42/1.06 { ! before_on_line( X, Y, Z ), distinct_points( Y, Z ) }.
% 0.42/1.06 { ! before_on_line( X, Y, Z ), alpha7( X, Y, Z ) }.
% 0.42/1.06 { ! distinct_points( Y, Z ), ! alpha7( X, Y, Z ), before_on_line( X, Y, Z )
% 0.42/1.06 }.
% 0.42/1.06 { ! alpha7( X, Y, Z ), alpha2( X, Y ) }.
% 0.42/1.06 { ! alpha7( X, Y, Z ), alpha8( X, Y, Z ) }.
% 0.42/1.06 { ! alpha2( X, Y ), ! alpha8( X, Y, Z ), alpha7( X, Y, Z ) }.
% 0.42/1.06 { ! alpha8( X, Y, Z ), alpha5( X, Z ) }.
% 0.42/1.06 { ! alpha8( X, Y, Z ), ! unequally_directed_lines( X, line_connecting( Y, Z
% 0.42/1.06 ) ) }.
% 0.42/1.06 { ! alpha5( X, Z ), unequally_directed_lines( X, line_connecting( Y, Z ) )
% 0.42/1.06 , alpha8( X, Y, Z ) }.
% 0.42/1.06 { ! alpha5( X, Y ), ! left_apart_point( Y, X ) }.
% 0.42/1.06 { ! alpha5( X, Y ), ! left_apart_point( Y, reverse_line( X ) ) }.
% 0.42/1.06 { left_apart_point( Y, X ), left_apart_point( Y, reverse_line( X ) ),
% 0.42/1.06 alpha5( X, Y ) }.
% 0.42/1.06 { ! alpha2( X, Y ), ! left_apart_point( Y, X ) }.
% 0.42/1.06 { ! alpha2( X, Y ), ! left_apart_point( Y, reverse_line( X ) ) }.
% 0.42/1.06 { left_apart_point( Y, X ), left_apart_point( Y, reverse_line( X ) ),
% 0.42/1.06 alpha2( X, Y ) }.
% 0.42/1.06 { ! between_on_line( X, Y, Z, T ), alpha3( X, Y, Z, T ), alpha6( X, Y, Z, T
% 0.42/1.06 ) }.
% 0.42/1.06 { ! alpha3( X, Y, Z, T ), between_on_line( X, Y, Z, T ) }.
% 0.42/1.06 { ! alpha6( X, Y, Z, T ), between_on_line( X, Y, Z, T ) }.
% 0.42/1.06 { ! alpha6( X, Y, Z, T ), before_on_line( X, T, Z ) }.
% 0.42/1.06 { ! alpha6( X, Y, Z, T ), before_on_line( X, Z, Y ) }.
% 0.42/1.06 { ! before_on_line( X, T, Z ), ! before_on_line( X, Z, Y ), alpha6( X, Y, Z
% 0.42/1.06 , T ) }.
% 0.42/1.06 { ! alpha3( X, Y, Z, T ), before_on_line( X, Y, Z ) }.
% 0.42/1.06 { ! alpha3( X, Y, Z, T ), before_on_line( X, Z, T ) }.
% 0.42/1.06 { ! before_on_line( X, Y, Z ), ! before_on_line( X, Z, T ), alpha3( X, Y, Z
% 0.42/1.06 , T ) }.
% 0.42/1.06 { ! distinct_points( X, X ) }.
% 0.42/1.06 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 0.42/1.06 ) }.
% 0.42/1.06 { ! distinct_lines( X, X ) }.
% 0.42/1.06 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.42/1.06 }.
% 0.42/1.06 { ! unequally_directed_lines( X, X ) }.
% 0.42/1.06 { ! unequally_directed_lines( X, Y ), unequally_directed_lines( X, Z ),
% 0.42/1.06 unequally_directed_lines( Y, Z ) }.
% 0.42/1.06 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.42/1.06 reverse_line( Y ) ), alpha9( X, Z ), unequally_directed_lines( Y, Z ) }.
% 0.42/1.06 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.42/1.06 reverse_line( Y ) ), alpha9( X, Z ), unequally_directed_lines( Y,
% 0.42/1.06 reverse_line( Z ) ) }.
% 0.42/1.06 { ! alpha9( X, Y ), unequally_directed_lines( X, Y ) }.
% 0.42/1.06 { ! alpha9( X, Y ), unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.42/1.06 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.42/1.06 reverse_line( Y ) ), alpha9( X, Y ) }.
% 0.42/1.06 { ! line( X ), ! line( Y ), unequally_directed_lines( X, Y ),
% 0.42/1.06 unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.42/1.06 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.42/1.06 reverse_line( Y ) ), left_convergent_lines( X, Y ), left_convergent_lines
% 0.42/1.06 ( X, reverse_line( Y ) ) }.
% 0.73/1.10 { ! left_apart_point( X, Y ) }.
% 0.73/1.10 { ! left_apart_point( X, reverse_line( Y ) ) }.
% 0.73/1.10 { ! left_convergent_lines( X, Y ) }.
% 0.73/1.10 { ! left_convergent_lines( X, reverse_line( Y ) ) }.
% 0.73/1.10 { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line(
% 0.73/1.10 line_connecting( X, Y ) ) }.
% 0.73/1.10 { ! line( X ), ! line( Y ), ! unequally_directed_lines( X, Y ), !
% 0.73/1.10 unequally_directed_lines( X, reverse_line( Y ) ), point(
% 0.73/1.10 intersection_point( X, Y ) ) }.
% 0.73/1.10 { ! point( Y ), ! line( X ), line( parallel_through_point( X, Y ) ) }.
% 0.73/1.10 { ! line( X ), line( reverse_line( X ) ) }.
% 0.73/1.10 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 0.73/1.10 , Y ) ) }.
% 0.73/1.10 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 0.73/1.10 , Y ) ) }.
% 0.73/1.10 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.73/1.10 reverse_line( Y ) ), ! apart_point_and_line( intersection_point( X, Y ),
% 0.73/1.10 X ) }.
% 0.73/1.10 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.73/1.10 reverse_line( Y ) ), ! apart_point_and_line( intersection_point( X, Y ),
% 0.73/1.10 Y ) }.
% 0.73/1.10 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 0.73/1.10 { ! distinct_lines( X, reverse_line( X ) ) }.
% 0.73/1.10 { ! unequally_directed_lines( line_connecting( X, Y ), reverse_line(
% 0.73/1.10 line_connecting( Y, X ) ) ) }.
% 0.73/1.10 { ! unequally_directed_lines( parallel_through_point( Y, X ), Y ) }.
% 0.73/1.10 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), left_apart_point( X
% 0.73/1.10 , Z ), left_apart_point( Y, Z ), left_apart_point( X, T ),
% 0.73/1.10 left_apart_point( Y, T ), left_apart_point( X, reverse_line( Z ) ),
% 0.73/1.10 left_apart_point( Y, reverse_line( Z ) ), left_apart_point( X,
% 0.73/1.10 reverse_line( T ) ), left_apart_point( Y, reverse_line( T ) ) }.
% 0.73/1.10 { ! distinct_points( X, Y ), ! left_apart_point( X, Z ), left_apart_point(
% 0.73/1.10 Y, Z ), left_convergent_lines( line_connecting( X, Y ), Z ) }.
% 0.73/1.10 { ! left_apart_point( X, Y ), distinct_points( X, Z ), left_apart_point( Z
% 0.73/1.10 , Y ) }.
% 0.73/1.10 { ! left_apart_point( X, Y ), ! unequally_directed_lines( Y, Z ),
% 0.73/1.10 distinct_lines( Y, Z ), left_apart_point( X, reverse_line( Z ) ) }.
% 0.73/1.10 { ! left_convergent_lines( X, Y ), unequally_directed_lines( Y, Z ),
% 0.73/1.10 left_convergent_lines( X, Z ) }.
% 0.73/1.10 { distinct_points( skol1, skol2 ) }.
% 0.73/1.10 { ! apart_point_and_line( skol1, skol3 ) }.
% 0.73/1.10 { ! apart_point_and_line( skol2, skol3 ) }.
% 0.73/1.10 { ! before_on_line( skol3, skol1, skol2 ), ! before_on_line( skol3, skol2,
% 0.73/1.10 skol1 ) }.
% 0.73/1.10
% 0.73/1.10 percentage equality = 0.000000, percentage horn = 0.802817
% 0.73/1.10 This a non-horn, non-equality problem
% 0.73/1.10
% 0.73/1.10
% 0.73/1.10 Options Used:
% 0.73/1.10
% 0.73/1.10 useres = 1
% 0.73/1.10 useparamod = 0
% 0.73/1.10 useeqrefl = 0
% 0.73/1.10 useeqfact = 0
% 0.73/1.10 usefactor = 1
% 0.73/1.10 usesimpsplitting = 0
% 0.73/1.10 usesimpdemod = 0
% 0.73/1.10 usesimpres = 3
% 0.73/1.10
% 0.73/1.10 resimpinuse = 1000
% 0.73/1.10 resimpclauses = 20000
% 0.73/1.10 substype = standard
% 0.73/1.10 backwardsubs = 1
% 0.73/1.10 selectoldest = 5
% 0.73/1.10
% 0.73/1.10 litorderings [0] = split
% 0.73/1.10 litorderings [1] = liftord
% 0.73/1.10
% 0.73/1.10 termordering = none
% 0.73/1.10
% 0.73/1.10 litapriori = 1
% 0.73/1.10 termapriori = 0
% 0.73/1.10 litaposteriori = 0
% 0.73/1.10 termaposteriori = 0
% 0.73/1.10 demodaposteriori = 0
% 0.73/1.10 ordereqreflfact = 0
% 0.73/1.10
% 0.73/1.10 litselect = none
% 0.73/1.10
% 0.73/1.10 maxweight = 15
% 0.73/1.10 maxdepth = 30000
% 0.73/1.10 maxlength = 115
% 0.73/1.10 maxnrvars = 195
% 0.73/1.10 excuselevel = 1
% 0.73/1.10 increasemaxweight = 1
% 0.73/1.10
% 0.73/1.10 maxselected = 10000000
% 0.73/1.10 maxnrclauses = 10000000
% 0.73/1.10
% 0.73/1.10 showgenerated = 0
% 0.73/1.10 showkept = 0
% 0.73/1.10 showselected = 0
% 0.73/1.10 showdeleted = 0
% 0.73/1.10 showresimp = 1
% 0.73/1.10 showstatus = 2000
% 0.73/1.10
% 0.73/1.10 prologoutput = 0
% 0.73/1.10 nrgoals = 5000000
% 0.73/1.10 totalproof = 1
% 0.73/1.10
% 0.73/1.10 Symbols occurring in the translation:
% 0.73/1.10
% 0.73/1.10 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.73/1.10 . [1, 2] (w:1, o:23, a:1, s:1, b:0),
% 0.73/1.10 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 0.73/1.10 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.73/1.10 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.73/1.10 apart_point_and_line [37, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.73/1.10 left_apart_point [38, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.73/1.10 reverse_line [39, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.73/1.10 convergent_lines [41, 2] (w:1, o:49, a:1, s:1, b:0),
% 0.73/1.10 unequally_directed_lines [42, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.73/1.10 divides_points [44, 3] (w:1, o:60, a:1, s:1, b:0),
% 0.73/1.10 before_on_line [45, 3] (w:1, o:65, a:1, s:1, b:0),
% 0.73/1.10 distinct_points [46, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.73/1.10 line_connecting [47, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.73/1.10 between_on_line [49, 4] (w:1, o:68, a:1, s:1, b:0),
% 0.73/1.10 distinct_lines [50, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.73/1.10 line [52, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.73/1.10 left_convergent_lines [53, 2] (w:1, o:54, a:1, s:1, b:0),
% 0.73/1.10 point [54, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.73/1.10 intersection_point [55, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.73/1.10 parallel_through_point [56, 2] (w:1, o:56, a:1, s:1, b:0),
% 0.73/1.10 alpha1 [57, 3] (w:1, o:61, a:1, s:1, b:0),
% 0.73/1.10 alpha2 [58, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.73/1.10 alpha3 [59, 4] (w:1, o:66, a:1, s:1, b:0),
% 0.73/1.10 alpha4 [60, 3] (w:1, o:62, a:1, s:1, b:0),
% 0.73/1.10 alpha5 [61, 2] (w:1, o:58, a:1, s:1, b:0),
% 0.73/1.10 alpha6 [62, 4] (w:1, o:67, a:1, s:1, b:0),
% 0.73/1.10 alpha7 [63, 3] (w:1, o:63, a:1, s:1, b:0),
% 0.73/1.10 alpha8 [64, 3] (w:1, o:64, a:1, s:1, b:0),
% 0.73/1.10 alpha9 [65, 2] (w:1, o:59, a:1, s:1, b:0),
% 0.73/1.10 skol1 [66, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.73/1.10 skol2 [67, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.73/1.10 skol3 [68, 0] (w:1, o:14, a:1, s:1, b:0).
% 0.73/1.10
% 0.73/1.10
% 0.73/1.10 Starting Search:
% 0.73/1.10
% 0.73/1.10 *** allocated 15000 integers for clauses
% 0.73/1.10 *** allocated 22500 integers for clauses
% 0.73/1.10 *** allocated 33750 integers for clauses
% 0.73/1.10 *** allocated 50625 integers for clauses
% 0.73/1.10 *** allocated 15000 integers for termspace/termends
% 0.73/1.10
% 0.73/1.10 Bliksems!, er is een bewijs:
% 0.73/1.10 % SZS status Theorem
% 0.73/1.10 % SZS output start Refutation
% 0.73/1.10
% 0.73/1.10 (17) {G0,W11,D2,L3,V3,M1} I { ! distinct_points( Y, Z ), ! alpha7( X, Y, Z
% 0.73/1.10 ), before_on_line( X, Y, Z ) }.
% 0.73/1.10 (20) {G0,W11,D2,L3,V3,M1} I { ! alpha2( X, Y ), alpha7( X, Y, Z ), ! alpha8
% 0.73/1.10 ( X, Y, Z ) }.
% 0.73/1.10 (23) {G0,W12,D3,L3,V3,M1} I { unequally_directed_lines( X, line_connecting
% 0.73/1.10 ( Y, Z ) ), ! alpha5( X, Z ), alpha8( X, Y, Z ) }.
% 0.73/1.10 (26) {G0,W10,D3,L3,V2,M1} I { left_apart_point( Y, X ), left_apart_point( Y
% 0.73/1.10 , reverse_line( X ) ), alpha5( X, Y ) }.
% 0.73/1.10 (29) {G0,W10,D3,L3,V2,M1} I { left_apart_point( Y, X ), left_apart_point( Y
% 0.73/1.10 , reverse_line( X ) ), alpha2( X, Y ) }.
% 0.73/1.10 (39) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 0.73/1.10 (40) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ), distinct_points( Y, Z
% 0.73/1.10 ), ! distinct_points( X, Y ) }.
% 0.73/1.10 (43) {G0,W3,D2,L1,V1,M1} I { ! unequally_directed_lines( X, X ) }.
% 0.73/1.10 (44) {G0,W9,D2,L3,V3,M3} I { unequally_directed_lines( X, Z ),
% 0.73/1.10 unequally_directed_lines( Y, Z ), ! unequally_directed_lines( X, Y ) }.
% 0.73/1.10 (51) {G0,W14,D3,L4,V2,M2} I { ! unequally_directed_lines( X, Y ), !
% 0.73/1.10 unequally_directed_lines( X, reverse_line( Y ) ), left_convergent_lines(
% 0.73/1.10 X, reverse_line( Y ) ), left_convergent_lines( X, Y ) }.
% 0.73/1.10 (52) {G0,W3,D2,L1,V2,M1} I { ! left_apart_point( X, Y ) }.
% 0.73/1.10 (53) {G0,W3,D2,L1,V2,M1} I { ! left_convergent_lines( X, Y ) }.
% 0.73/1.10 (64) {G0,W8,D4,L1,V2,M1} I { ! unequally_directed_lines( line_connecting( X
% 0.73/1.10 , Y ), reverse_line( line_connecting( Y, X ) ) ) }.
% 0.73/1.10 (65) {G0,W5,D3,L1,V2,M1} I { ! unequally_directed_lines(
% 0.73/1.10 parallel_through_point( Y, X ), Y ) }.
% 0.73/1.10 (67) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol1, skol2 ) }.
% 0.73/1.10 (70) {G0,W8,D2,L2,V0,M1} I { ! before_on_line( skol3, skol2, skol1 ), !
% 0.73/1.10 before_on_line( skol3, skol1, skol2 ) }.
% 0.73/1.10 (96) {G1,W8,D2,L2,V0,M1} R(17,70);r(67) { ! alpha7( skol3, skol1, skol2 ),
% 0.73/1.10 ! before_on_line( skol3, skol2, skol1 ) }.
% 0.73/1.10 (97) {G2,W11,D2,L3,V0,M1} R(96,17) { ! distinct_points( skol2, skol1 ), !
% 0.73/1.10 alpha7( skol3, skol2, skol1 ), ! alpha7( skol3, skol1, skol2 ) }.
% 0.73/1.10 (111) {G1,W6,D2,L2,V2,M2} R(44,43) { ! unequally_directed_lines( Y, X ),
% 0.73/1.10 unequally_directed_lines( X, Y ) }.
% 0.73/1.10 (122) {G2,W5,D3,L1,V2,M1} R(111,65) { ! unequally_directed_lines( X,
% 0.73/1.10 parallel_through_point( X, Y ) ) }.
% 0.73/1.10 (124) {G3,W8,D3,L2,V3,M2} R(122,44) { ! unequally_directed_lines( Y, X ),
% 0.73/1.10 unequally_directed_lines( X, parallel_through_point( Y, Z ) ) }.
% 0.73/1.10 (131) {G1,W15,D3,L4,V3,M1} R(23,20) { unequally_directed_lines( X,
% 0.73/1.10 line_connecting( Y, Z ) ), ! alpha2( X, Y ), ! alpha5( X, Z ), alpha7( X
% 0.73/1.10 , Y, Z ) }.
% 0.73/1.10 (153) {G1,W3,D2,L1,V2,M1} S(26);r(52);r(52) { alpha5( X, Y ) }.
% 0.73/1.10 (162) {G1,W3,D2,L1,V2,M1} S(29);r(52);r(52) { alpha2( X, Y ) }.
% 0.73/1.10 (288) {G1,W6,D2,L2,V2,M2} R(40,39) { ! distinct_points( Y, X ),
% 0.73/1.10 distinct_points( X, Y ) }.
% 0.73/1.10 (291) {G2,W3,D2,L1,V0,M1} R(288,67) { distinct_points( skol2, skol1 ) }.
% 0.73/1.10 (401) {G1,W7,D3,L2,V2,M2} S(51);r(53);r(53) { ! unequally_directed_lines( X
% 0.73/1.10 , reverse_line( Y ) ), ! unequally_directed_lines( X, Y ) }.
% 0.73/1.10 (433) {G2,W7,D3,L2,V2,M2} R(401,111) { ! unequally_directed_lines( Y, X ),
% 0.73/1.10 ! unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.73/1.10 (489) {G3,W10,D3,L3,V3,M3} R(433,44) { unequally_directed_lines( Z,
% 0.73/1.10 reverse_line( X ) ), ! unequally_directed_lines( Z, Y ), !
% 0.73/1.10 unequally_directed_lines( X, Y ) }.
% 0.73/1.10 (490) {G4,W7,D3,L2,V2,M2} F(489) { ! unequally_directed_lines( X, Y ),
% 0.73/1.10 unequally_directed_lines( X, reverse_line( X ) ) }.
% 0.73/1.10 (510) {G5,W5,D3,L1,V2,M1} R(490,64) { ! unequally_directed_lines(
% 0.73/1.10 line_connecting( X, X ), Y ) }.
% 0.73/1.10 (515) {G6,W5,D3,L1,V2,M1} R(510,124) { ! unequally_directed_lines( X,
% 0.73/1.10 line_connecting( Y, Y ) ) }.
% 0.73/1.10 (516) {G7,W3,D2,L1,V2,M1} R(515,44);r(515) { ! unequally_directed_lines( Z
% 0.73/1.10 , X ) }.
% 0.73/1.10 (666) {G3,W8,D2,L2,V0,M1} S(97);r(291) { ! alpha7( skol3, skol2, skol1 ), !
% 0.73/1.10 alpha7( skol3, skol1, skol2 ) }.
% 0.73/1.10 (771) {G8,W4,D2,L1,V3,M1} S(131);r(516);r(162);r(153) { alpha7( X, Y, Z )
% 0.73/1.10 }.
% 0.73/1.10 (772) {G9,W0,D0,L0,V0,M0} R(771,666);r(771) { }.
% 0.73/1.10
% 0.73/1.10
% 0.73/1.10 % SZS output end Refutation
% 0.73/1.10 found a proof!
% 0.73/1.10
% 0.73/1.10
% 0.73/1.10 Unprocessed initial clauses:
% 0.73/1.10
% 0.73/1.10 (774) {G0,W10,D3,L3,V2,M3} { ! apart_point_and_line( X, Y ),
% 0.73/1.10 left_apart_point( X, Y ), left_apart_point( X, reverse_line( Y ) ) }.
% 0.73/1.10 (775) {G0,W6,D2,L2,V2,M2} { ! left_apart_point( X, Y ),
% 0.73/1.10 apart_point_and_line( X, Y ) }.
% 0.73/1.10 (776) {G0,W7,D3,L2,V2,M2} { ! left_apart_point( X, reverse_line( Y ) ),
% 0.73/1.10 apart_point_and_line( X, Y ) }.
% 0.73/1.10 (777) {G0,W6,D2,L2,V2,M2} { ! convergent_lines( X, Y ),
% 0.73/1.10 unequally_directed_lines( X, Y ) }.
% 0.73/1.10 (778) {G0,W7,D3,L2,V2,M2} { ! convergent_lines( X, Y ),
% 0.73/1.10 unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.73/1.10 (779) {G0,W10,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y ), !
% 0.73/1.10 unequally_directed_lines( X, reverse_line( Y ) ), convergent_lines( X, Y
% 0.73/1.10 ) }.
% 0.73/1.10 (780) {G0,W12,D2,L3,V3,M3} { ! divides_points( Z, X, Y ), alpha1( X, Y, Z
% 0.73/1.10 ), alpha4( X, Y, Z ) }.
% 0.73/1.10 (781) {G0,W8,D2,L2,V3,M2} { ! alpha1( X, Y, Z ), divides_points( Z, X, Y )
% 0.73/1.10 }.
% 0.73/1.10 (782) {G0,W8,D2,L2,V3,M2} { ! alpha4( X, Y, Z ), divides_points( Z, X, Y )
% 0.73/1.10 }.
% 0.73/1.10 (783) {G0,W8,D3,L2,V3,M2} { ! alpha4( X, Y, Z ), left_apart_point( X,
% 0.73/1.10 reverse_line( Z ) ) }.
% 0.73/1.10 (784) {G0,W7,D2,L2,V3,M2} { ! alpha4( X, Y, Z ), left_apart_point( Y, Z )
% 0.73/1.10 }.
% 0.73/1.10 (785) {G0,W11,D3,L3,V3,M3} { ! left_apart_point( X, reverse_line( Z ) ), !
% 0.73/1.10 left_apart_point( Y, Z ), alpha4( X, Y, Z ) }.
% 0.73/1.10 (786) {G0,W7,D2,L2,V3,M2} { ! alpha1( X, Y, Z ), left_apart_point( X, Z )
% 0.73/1.10 }.
% 0.73/1.10 (787) {G0,W8,D3,L2,V3,M2} { ! alpha1( X, Y, Z ), left_apart_point( Y,
% 0.73/1.10 reverse_line( Z ) ) }.
% 0.73/1.10 (788) {G0,W11,D3,L3,V3,M3} { ! left_apart_point( X, Z ), !
% 0.73/1.10 left_apart_point( Y, reverse_line( Z ) ), alpha1( X, Y, Z ) }.
% 0.73/1.10 (789) {G0,W7,D2,L2,V3,M2} { ! before_on_line( X, Y, Z ), distinct_points(
% 0.73/1.10 Y, Z ) }.
% 0.73/1.10 (790) {G0,W8,D2,L2,V3,M2} { ! before_on_line( X, Y, Z ), alpha7( X, Y, Z )
% 0.73/1.10 }.
% 0.73/1.10 (791) {G0,W11,D2,L3,V3,M3} { ! distinct_points( Y, Z ), ! alpha7( X, Y, Z
% 0.73/1.10 ), before_on_line( X, Y, Z ) }.
% 0.73/1.10 (792) {G0,W7,D2,L2,V3,M2} { ! alpha7( X, Y, Z ), alpha2( X, Y ) }.
% 0.73/1.10 (793) {G0,W8,D2,L2,V3,M2} { ! alpha7( X, Y, Z ), alpha8( X, Y, Z ) }.
% 0.73/1.10 (794) {G0,W11,D2,L3,V3,M3} { ! alpha2( X, Y ), ! alpha8( X, Y, Z ), alpha7
% 0.73/1.10 ( X, Y, Z ) }.
% 0.73/1.10 (795) {G0,W7,D2,L2,V3,M2} { ! alpha8( X, Y, Z ), alpha5( X, Z ) }.
% 0.73/1.10 (796) {G0,W9,D3,L2,V3,M2} { ! alpha8( X, Y, Z ), !
% 0.73/1.10 unequally_directed_lines( X, line_connecting( Y, Z ) ) }.
% 0.73/1.10 (797) {G0,W12,D3,L3,V3,M3} { ! alpha5( X, Z ), unequally_directed_lines( X
% 0.73/1.10 , line_connecting( Y, Z ) ), alpha8( X, Y, Z ) }.
% 0.73/1.10 (798) {G0,W6,D2,L2,V2,M2} { ! alpha5( X, Y ), ! left_apart_point( Y, X )
% 0.73/1.10 }.
% 0.73/1.10 (799) {G0,W7,D3,L2,V2,M2} { ! alpha5( X, Y ), ! left_apart_point( Y,
% 0.73/1.10 reverse_line( X ) ) }.
% 0.73/1.10 (800) {G0,W10,D3,L3,V2,M3} { left_apart_point( Y, X ), left_apart_point( Y
% 0.73/1.10 , reverse_line( X ) ), alpha5( X, Y ) }.
% 0.73/1.10 (801) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), ! left_apart_point( Y, X )
% 0.73/1.10 }.
% 0.73/1.10 (802) {G0,W7,D3,L2,V2,M2} { ! alpha2( X, Y ), ! left_apart_point( Y,
% 0.73/1.10 reverse_line( X ) ) }.
% 0.73/1.10 (803) {G0,W10,D3,L3,V2,M3} { left_apart_point( Y, X ), left_apart_point( Y
% 0.73/1.10 , reverse_line( X ) ), alpha2( X, Y ) }.
% 0.73/1.10 (804) {G0,W15,D2,L3,V4,M3} { ! between_on_line( X, Y, Z, T ), alpha3( X, Y
% 0.73/1.10 , Z, T ), alpha6( X, Y, Z, T ) }.
% 0.73/1.10 (805) {G0,W10,D2,L2,V4,M2} { ! alpha3( X, Y, Z, T ), between_on_line( X, Y
% 0.73/1.10 , Z, T ) }.
% 0.73/1.10 (806) {G0,W10,D2,L2,V4,M2} { ! alpha6( X, Y, Z, T ), between_on_line( X, Y
% 0.73/1.10 , Z, T ) }.
% 0.73/1.10 (807) {G0,W9,D2,L2,V4,M2} { ! alpha6( X, Y, Z, T ), before_on_line( X, T,
% 0.73/1.10 Z ) }.
% 0.73/1.10 (808) {G0,W9,D2,L2,V4,M2} { ! alpha6( X, Y, Z, T ), before_on_line( X, Z,
% 0.73/1.10 Y ) }.
% 0.73/1.10 (809) {G0,W13,D2,L3,V4,M3} { ! before_on_line( X, T, Z ), ! before_on_line
% 0.73/1.10 ( X, Z, Y ), alpha6( X, Y, Z, T ) }.
% 0.73/1.10 (810) {G0,W9,D2,L2,V4,M2} { ! alpha3( X, Y, Z, T ), before_on_line( X, Y,
% 0.73/1.10 Z ) }.
% 0.73/1.10 (811) {G0,W9,D2,L2,V4,M2} { ! alpha3( X, Y, Z, T ), before_on_line( X, Z,
% 0.73/1.10 T ) }.
% 0.73/1.10 (812) {G0,W13,D2,L3,V4,M3} { ! before_on_line( X, Y, Z ), ! before_on_line
% 0.73/1.10 ( X, Z, T ), alpha3( X, Y, Z, T ) }.
% 0.73/1.10 (813) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 0.73/1.10 (814) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 0.73/1.10 , Z ), distinct_points( Y, Z ) }.
% 0.73/1.10 (815) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.73/1.10 (816) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X, Z
% 0.73/1.10 ), distinct_lines( Y, Z ) }.
% 0.73/1.10 (817) {G0,W3,D2,L1,V1,M1} { ! unequally_directed_lines( X, X ) }.
% 0.73/1.10 (818) {G0,W9,D2,L3,V3,M3} { ! unequally_directed_lines( X, Y ),
% 0.73/1.10 unequally_directed_lines( X, Z ), unequally_directed_lines( Y, Z ) }.
% 0.73/1.10 (819) {G0,W13,D3,L4,V3,M4} { ! unequally_directed_lines( X, Y ), !
% 0.73/1.10 unequally_directed_lines( X, reverse_line( Y ) ), alpha9( X, Z ),
% 0.73/1.10 unequally_directed_lines( Y, Z ) }.
% 0.73/1.10 (820) {G0,W14,D3,L4,V3,M4} { ! unequally_directed_lines( X, Y ), !
% 0.73/1.10 unequally_directed_lines( X, reverse_line( Y ) ), alpha9( X, Z ),
% 0.73/1.10 unequally_directed_lines( Y, reverse_line( Z ) ) }.
% 0.73/1.10 (821) {G0,W6,D2,L2,V2,M2} { ! alpha9( X, Y ), unequally_directed_lines( X
% 0.73/1.10 , Y ) }.
% 0.73/1.10 (822) {G0,W7,D3,L2,V2,M2} { ! alpha9( X, Y ), unequally_directed_lines( X
% 0.73/1.10 , reverse_line( Y ) ) }.
% 0.73/1.10 (823) {G0,W10,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y ), !
% 0.73/1.10 unequally_directed_lines( X, reverse_line( Y ) ), alpha9( X, Y ) }.
% 0.73/1.10 (824) {G0,W11,D3,L4,V2,M4} { ! line( X ), ! line( Y ),
% 0.73/1.10 unequally_directed_lines( X, Y ), unequally_directed_lines( X,
% 0.73/1.10 reverse_line( Y ) ) }.
% 0.73/1.10 (825) {G0,W14,D3,L4,V2,M4} { ! unequally_directed_lines( X, Y ), !
% 0.73/1.10 unequally_directed_lines( X, reverse_line( Y ) ), left_convergent_lines(
% 0.73/1.10 X, Y ), left_convergent_lines( X, reverse_line( Y ) ) }.
% 0.73/1.10 (826) {G0,W3,D2,L1,V2,M1} { ! left_apart_point( X, Y ) }.
% 0.73/1.10 (827) {G0,W4,D3,L1,V2,M1} { ! left_apart_point( X, reverse_line( Y ) ) }.
% 0.73/1.10 (828) {G0,W3,D2,L1,V2,M1} { ! left_convergent_lines( X, Y ) }.
% 0.73/1.10 (829) {G0,W4,D3,L1,V2,M1} { ! left_convergent_lines( X, reverse_line( Y )
% 0.73/1.10 ) }.
% 0.73/1.10 (830) {G0,W11,D3,L4,V2,M4} { ! point( X ), ! point( Y ), ! distinct_points
% 0.73/1.10 ( X, Y ), line( line_connecting( X, Y ) ) }.
% 0.73/1.10 (831) {G0,W15,D3,L5,V2,M5} { ! line( X ), ! line( Y ), !
% 0.73/1.10 unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.73/1.10 reverse_line( Y ) ), point( intersection_point( X, Y ) ) }.
% 0.73/1.10 (832) {G0,W8,D3,L3,V2,M3} { ! point( Y ), ! line( X ), line(
% 0.73/1.10 parallel_through_point( X, Y ) ) }.
% 0.73/1.10 (833) {G0,W5,D3,L2,V1,M2} { ! line( X ), line( reverse_line( X ) ) }.
% 0.73/1.10 (834) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.73/1.10 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 0.73/1.10 (835) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.73/1.10 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 0.73/1.10 (836) {G0,W12,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y ), !
% 0.73/1.10 unequally_directed_lines( X, reverse_line( Y ) ), ! apart_point_and_line
% 0.73/1.10 ( intersection_point( X, Y ), X ) }.
% 0.73/1.10 (837) {G0,W12,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y ), !
% 0.73/1.10 unequally_directed_lines( X, reverse_line( Y ) ), ! apart_point_and_line
% 0.73/1.10 ( intersection_point( X, Y ), Y ) }.
% 0.73/1.10 (838) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.73/1.10 parallel_through_point( Y, X ) ) }.
% 0.73/1.10 (839) {G0,W4,D3,L1,V1,M1} { ! distinct_lines( X, reverse_line( X ) ) }.
% 0.73/1.10 (840) {G0,W8,D4,L1,V2,M1} { ! unequally_directed_lines( line_connecting( X
% 0.73/1.10 , Y ), reverse_line( line_connecting( Y, X ) ) ) }.
% 0.73/1.10 (841) {G0,W5,D3,L1,V2,M1} { ! unequally_directed_lines(
% 0.73/1.10 parallel_through_point( Y, X ), Y ) }.
% 0.73/1.10 (842) {G0,W34,D3,L10,V4,M10} { ! distinct_points( X, Y ), ! distinct_lines
% 0.73/1.10 ( Z, T ), left_apart_point( X, Z ), left_apart_point( Y, Z ),
% 0.73/1.10 left_apart_point( X, T ), left_apart_point( Y, T ), left_apart_point( X,
% 0.73/1.10 reverse_line( Z ) ), left_apart_point( Y, reverse_line( Z ) ),
% 0.73/1.10 left_apart_point( X, reverse_line( T ) ), left_apart_point( Y,
% 0.73/1.10 reverse_line( T ) ) }.
% 0.73/1.10 (843) {G0,W14,D3,L4,V3,M4} { ! distinct_points( X, Y ), ! left_apart_point
% 0.73/1.10 ( X, Z ), left_apart_point( Y, Z ), left_convergent_lines(
% 0.73/1.10 line_connecting( X, Y ), Z ) }.
% 0.73/1.10 (844) {G0,W9,D2,L3,V3,M3} { ! left_apart_point( X, Y ), distinct_points( X
% 0.73/1.10 , Z ), left_apart_point( Z, Y ) }.
% 0.73/1.10 (845) {G0,W13,D3,L4,V3,M4} { ! left_apart_point( X, Y ), !
% 0.73/1.10 unequally_directed_lines( Y, Z ), distinct_lines( Y, Z ),
% 0.73/1.10 left_apart_point( X, reverse_line( Z ) ) }.
% 0.73/1.10 (846) {G0,W9,D2,L3,V3,M3} { ! left_convergent_lines( X, Y ),
% 0.73/1.10 unequally_directed_lines( Y, Z ), left_convergent_lines( X, Z ) }.
% 0.73/1.10 (847) {G0,W3,D2,L1,V0,M1} { distinct_points( skol1, skol2 ) }.
% 0.73/1.10 (848) {G0,W3,D2,L1,V0,M1} { ! apart_point_and_line( skol1, skol3 ) }.
% 0.73/1.10 (849) {G0,W3,D2,L1,V0,M1} { ! apart_point_and_line( skol2, skol3 ) }.
% 0.73/1.10 (850) {G0,W8,D2,L2,V0,M2} { ! before_on_line( skol3, skol1, skol2 ), !
% 0.73/1.10 before_on_line( skol3, skol2, skol1 ) }.
% 0.73/1.10
% 0.73/1.10
% 0.73/1.10 Total Proof:
% 0.73/1.10
% 0.73/1.10 subsumption: (17) {G0,W11,D2,L3,V3,M1} I { ! distinct_points( Y, Z ), !
% 0.73/1.10 alpha7( X, Y, Z ), before_on_line( X, Y, Z ) }.
% 0.73/1.10 parent0: (791) {G0,W11,D2,L3,V3,M3} { ! distinct_points( Y, Z ), ! alpha7
% 0.73/1.10 ( X, Y, Z ), before_on_line( X, Y, Z ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 X := X
% 0.73/1.10 Y := Y
% 0.73/1.10 Z := Z
% 0.73/1.10 end
% 0.73/1.10 permutation0:
% 0.73/1.10 0 ==> 0
% 0.73/1.10 1 ==> 1
% 0.73/1.10 2 ==> 2
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 subsumption: (20) {G0,W11,D2,L3,V3,M1} I { ! alpha2( X, Y ), alpha7( X, Y,
% 0.73/1.10 Z ), ! alpha8( X, Y, Z ) }.
% 0.73/1.10 parent0: (794) {G0,W11,D2,L3,V3,M3} { ! alpha2( X, Y ), ! alpha8( X, Y, Z
% 0.73/1.10 ), alpha7( X, Y, Z ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 X := X
% 0.73/1.10 Y := Y
% 0.73/1.10 Z := Z
% 0.73/1.10 end
% 0.73/1.10 permutation0:
% 0.73/1.10 0 ==> 0
% 0.73/1.10 1 ==> 2
% 0.73/1.10 2 ==> 1
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 subsumption: (23) {G0,W12,D3,L3,V3,M1} I { unequally_directed_lines( X,
% 0.73/1.10 line_connecting( Y, Z ) ), ! alpha5( X, Z ), alpha8( X, Y, Z ) }.
% 0.73/1.10 parent0: (797) {G0,W12,D3,L3,V3,M3} { ! alpha5( X, Z ),
% 0.73/1.10 unequally_directed_lines( X, line_connecting( Y, Z ) ), alpha8( X, Y, Z )
% 0.73/1.10 }.
% 0.73/1.10 substitution0:
% 0.73/1.10 X := X
% 0.73/1.10 Y := Y
% 0.73/1.10 Z := Z
% 0.73/1.10 end
% 0.73/1.10 permutation0:
% 0.73/1.10 0 ==> 1
% 0.73/1.10 1 ==> 0
% 0.73/1.10 2 ==> 2
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 subsumption: (26) {G0,W10,D3,L3,V2,M1} I { left_apart_point( Y, X ),
% 0.73/1.10 left_apart_point( Y, reverse_line( X ) ), alpha5( X, Y ) }.
% 0.73/1.10 parent0: (800) {G0,W10,D3,L3,V2,M3} { left_apart_point( Y, X ),
% 0.73/1.10 left_apart_point( Y, reverse_line( X ) ), alpha5( X, Y ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 X := X
% 0.73/1.10 Y := Y
% 0.73/1.10 end
% 0.73/1.10 permutation0:
% 0.73/1.10 0 ==> 0
% 0.73/1.10 1 ==> 1
% 0.73/1.10 2 ==> 2
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 subsumption: (29) {G0,W10,D3,L3,V2,M1} I { left_apart_point( Y, X ),
% 0.73/1.10 left_apart_point( Y, reverse_line( X ) ), alpha2( X, Y ) }.
% 0.73/1.10 parent0: (803) {G0,W10,D3,L3,V2,M3} { left_apart_point( Y, X ),
% 0.73/1.10 left_apart_point( Y, reverse_line( X ) ), alpha2( X, Y ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 X := X
% 0.73/1.10 Y := Y
% 0.73/1.10 end
% 0.73/1.10 permutation0:
% 0.73/1.10 0 ==> 0
% 0.73/1.10 1 ==> 1
% 0.73/1.10 2 ==> 2
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 subsumption: (39) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 0.73/1.10 parent0: (813) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 X := X
% 0.73/1.10 end
% 0.73/1.10 permutation0:
% 0.73/1.10 0 ==> 0
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 subsumption: (40) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ),
% 0.73/1.10 distinct_points( Y, Z ), ! distinct_points( X, Y ) }.
% 0.73/1.10 parent0: (814) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ),
% 0.73/1.10 distinct_points( X, Z ), distinct_points( Y, Z ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 X := X
% 0.73/1.10 Y := Y
% 0.73/1.10 Z := Z
% 0.73/1.10 end
% 0.73/1.10 permutation0:
% 0.73/1.10 0 ==> 2
% 0.73/1.10 1 ==> 0
% 0.73/1.10 2 ==> 1
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 subsumption: (43) {G0,W3,D2,L1,V1,M1} I { ! unequally_directed_lines( X, X
% 0.73/1.10 ) }.
% 0.73/1.10 parent0: (817) {G0,W3,D2,L1,V1,M1} { ! unequally_directed_lines( X, X )
% 0.73/1.10 }.
% 0.73/1.10 substitution0:
% 0.73/1.10 X := X
% 0.73/1.10 end
% 0.73/1.10 permutation0:
% 0.73/1.10 0 ==> 0
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 subsumption: (44) {G0,W9,D2,L3,V3,M3} I { unequally_directed_lines( X, Z )
% 0.73/1.10 , unequally_directed_lines( Y, Z ), ! unequally_directed_lines( X, Y )
% 0.73/1.10 }.
% 0.73/1.10 parent0: (818) {G0,W9,D2,L3,V3,M3} { ! unequally_directed_lines( X, Y ),
% 0.73/1.10 unequally_directed_lines( X, Z ), unequally_directed_lines( Y, Z ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 X := X
% 0.73/1.10 Y := Y
% 0.73/1.10 Z := Z
% 0.73/1.10 end
% 0.73/1.10 permutation0:
% 0.73/1.10 0 ==> 2
% 0.73/1.10 1 ==> 0
% 0.73/1.10 2 ==> 1
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 subsumption: (51) {G0,W14,D3,L4,V2,M2} I { ! unequally_directed_lines( X, Y
% 0.73/1.10 ), ! unequally_directed_lines( X, reverse_line( Y ) ),
% 0.73/1.10 left_convergent_lines( X, reverse_line( Y ) ), left_convergent_lines( X,
% 0.73/1.10 Y ) }.
% 0.73/1.10 parent0: (825) {G0,W14,D3,L4,V2,M4} { ! unequally_directed_lines( X, Y ),
% 0.73/1.10 ! unequally_directed_lines( X, reverse_line( Y ) ), left_convergent_lines
% 0.73/1.10 ( X, Y ), left_convergent_lines( X, reverse_line( Y ) ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 X := X
% 0.73/1.10 Y := Y
% 0.73/1.10 end
% 0.73/1.10 permutation0:
% 0.73/1.10 0 ==> 0
% 0.73/1.10 1 ==> 1
% 0.73/1.10 2 ==> 3
% 0.73/1.10 3 ==> 2
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 subsumption: (52) {G0,W3,D2,L1,V2,M1} I { ! left_apart_point( X, Y ) }.
% 0.73/1.10 parent0: (826) {G0,W3,D2,L1,V2,M1} { ! left_apart_point( X, Y ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 X := X
% 0.73/1.10 Y := Y
% 0.73/1.10 end
% 0.73/1.10 permutation0:
% 0.73/1.10 0 ==> 0
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 subsumption: (53) {G0,W3,D2,L1,V2,M1} I { ! left_convergent_lines( X, Y )
% 0.73/1.10 }.
% 0.73/1.10 parent0: (828) {G0,W3,D2,L1,V2,M1} { ! left_convergent_lines( X, Y ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 X := X
% 0.73/1.10 Y := Y
% 0.73/1.10 end
% 0.73/1.10 permutation0:
% 0.73/1.10 0 ==> 0
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 subsumption: (64) {G0,W8,D4,L1,V2,M1} I { ! unequally_directed_lines(
% 0.73/1.10 line_connecting( X, Y ), reverse_line( line_connecting( Y, X ) ) ) }.
% 0.73/1.10 parent0: (840) {G0,W8,D4,L1,V2,M1} { ! unequally_directed_lines(
% 0.73/1.10 line_connecting( X, Y ), reverse_line( line_connecting( Y, X ) ) ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 X := X
% 0.73/1.10 Y := Y
% 0.73/1.10 end
% 0.73/1.10 permutation0:
% 0.73/1.10 0 ==> 0
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 subsumption: (65) {G0,W5,D3,L1,V2,M1} I { ! unequally_directed_lines(
% 0.73/1.10 parallel_through_point( Y, X ), Y ) }.
% 0.73/1.10 parent0: (841) {G0,W5,D3,L1,V2,M1} { ! unequally_directed_lines(
% 0.73/1.10 parallel_through_point( Y, X ), Y ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 X := X
% 0.73/1.10 Y := Y
% 0.73/1.10 end
% 0.73/1.10 permutation0:
% 0.73/1.10 0 ==> 0
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 subsumption: (67) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol1, skol2 )
% 0.73/1.10 }.
% 0.73/1.10 parent0: (847) {G0,W3,D2,L1,V0,M1} { distinct_points( skol1, skol2 ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 end
% 0.73/1.10 permutation0:
% 0.73/1.10 0 ==> 0
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 subsumption: (70) {G0,W8,D2,L2,V0,M1} I { ! before_on_line( skol3, skol2,
% 0.73/1.10 skol1 ), ! before_on_line( skol3, skol1, skol2 ) }.
% 0.73/1.10 parent0: (850) {G0,W8,D2,L2,V0,M2} { ! before_on_line( skol3, skol1, skol2
% 0.73/1.10 ), ! before_on_line( skol3, skol2, skol1 ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 end
% 0.73/1.10 permutation0:
% 0.73/1.10 0 ==> 1
% 0.73/1.10 1 ==> 0
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 resolution: (968) {G1,W11,D2,L3,V0,M3} { ! before_on_line( skol3, skol2,
% 0.73/1.10 skol1 ), ! distinct_points( skol1, skol2 ), ! alpha7( skol3, skol1, skol2
% 0.73/1.10 ) }.
% 0.73/1.10 parent0[1]: (70) {G0,W8,D2,L2,V0,M1} I { ! before_on_line( skol3, skol2,
% 0.73/1.10 skol1 ), ! before_on_line( skol3, skol1, skol2 ) }.
% 0.73/1.10 parent1[2]: (17) {G0,W11,D2,L3,V3,M1} I { ! distinct_points( Y, Z ), !
% 0.73/1.10 alpha7( X, Y, Z ), before_on_line( X, Y, Z ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 end
% 0.73/1.10 substitution1:
% 0.73/1.10 X := skol3
% 0.73/1.10 Y := skol1
% 0.73/1.10 Z := skol2
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 resolution: (969) {G1,W8,D2,L2,V0,M2} { ! before_on_line( skol3, skol2,
% 0.73/1.10 skol1 ), ! alpha7( skol3, skol1, skol2 ) }.
% 0.73/1.10 parent0[1]: (968) {G1,W11,D2,L3,V0,M3} { ! before_on_line( skol3, skol2,
% 0.73/1.10 skol1 ), ! distinct_points( skol1, skol2 ), ! alpha7( skol3, skol1, skol2
% 0.73/1.10 ) }.
% 0.73/1.10 parent1[0]: (67) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol1, skol2 )
% 0.73/1.10 }.
% 0.73/1.10 substitution0:
% 0.73/1.10 end
% 0.73/1.10 substitution1:
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 subsumption: (96) {G1,W8,D2,L2,V0,M1} R(17,70);r(67) { ! alpha7( skol3,
% 0.73/1.10 skol1, skol2 ), ! before_on_line( skol3, skol2, skol1 ) }.
% 0.73/1.10 parent0: (969) {G1,W8,D2,L2,V0,M2} { ! before_on_line( skol3, skol2, skol1
% 0.73/1.10 ), ! alpha7( skol3, skol1, skol2 ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 end
% 0.73/1.10 permutation0:
% 0.73/1.10 0 ==> 1
% 0.73/1.10 1 ==> 0
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 resolution: (970) {G1,W11,D2,L3,V0,M3} { ! alpha7( skol3, skol1, skol2 ),
% 0.73/1.10 ! distinct_points( skol2, skol1 ), ! alpha7( skol3, skol2, skol1 ) }.
% 0.73/1.10 parent0[1]: (96) {G1,W8,D2,L2,V0,M1} R(17,70);r(67) { ! alpha7( skol3,
% 0.73/1.10 skol1, skol2 ), ! before_on_line( skol3, skol2, skol1 ) }.
% 0.73/1.10 parent1[2]: (17) {G0,W11,D2,L3,V3,M1} I { ! distinct_points( Y, Z ), !
% 0.73/1.10 alpha7( X, Y, Z ), before_on_line( X, Y, Z ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 end
% 0.73/1.10 substitution1:
% 0.73/1.10 X := skol3
% 0.73/1.10 Y := skol2
% 0.73/1.10 Z := skol1
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 subsumption: (97) {G2,W11,D2,L3,V0,M1} R(96,17) { ! distinct_points( skol2
% 0.73/1.10 , skol1 ), ! alpha7( skol3, skol2, skol1 ), ! alpha7( skol3, skol1, skol2
% 0.73/1.10 ) }.
% 0.73/1.10 parent0: (970) {G1,W11,D2,L3,V0,M3} { ! alpha7( skol3, skol1, skol2 ), !
% 0.73/1.10 distinct_points( skol2, skol1 ), ! alpha7( skol3, skol2, skol1 ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 end
% 0.73/1.10 permutation0:
% 0.73/1.10 0 ==> 2
% 0.73/1.10 1 ==> 0
% 0.73/1.10 2 ==> 1
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 resolution: (971) {G1,W6,D2,L2,V2,M2} { unequally_directed_lines( Y, X ),
% 0.73/1.10 ! unequally_directed_lines( X, Y ) }.
% 0.73/1.10 parent0[0]: (43) {G0,W3,D2,L1,V1,M1} I { ! unequally_directed_lines( X, X )
% 0.73/1.10 }.
% 0.73/1.10 parent1[0]: (44) {G0,W9,D2,L3,V3,M3} I { unequally_directed_lines( X, Z ),
% 0.73/1.10 unequally_directed_lines( Y, Z ), ! unequally_directed_lines( X, Y ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 X := X
% 0.73/1.10 end
% 0.73/1.10 substitution1:
% 0.73/1.10 X := X
% 0.73/1.10 Y := Y
% 0.73/1.10 Z := X
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 subsumption: (111) {G1,W6,D2,L2,V2,M2} R(44,43) { !
% 0.73/1.10 unequally_directed_lines( Y, X ), unequally_directed_lines( X, Y ) }.
% 0.73/1.10 parent0: (971) {G1,W6,D2,L2,V2,M2} { unequally_directed_lines( Y, X ), !
% 0.73/1.10 unequally_directed_lines( X, Y ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 X := Y
% 0.73/1.10 Y := X
% 0.73/1.10 end
% 0.73/1.10 permutation0:
% 0.73/1.10 0 ==> 1
% 0.73/1.10 1 ==> 0
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 resolution: (973) {G1,W5,D3,L1,V2,M1} { ! unequally_directed_lines( X,
% 0.73/1.10 parallel_through_point( X, Y ) ) }.
% 0.73/1.10 parent0[0]: (65) {G0,W5,D3,L1,V2,M1} I { ! unequally_directed_lines(
% 0.73/1.10 parallel_through_point( Y, X ), Y ) }.
% 0.73/1.10 parent1[1]: (111) {G1,W6,D2,L2,V2,M2} R(44,43) { ! unequally_directed_lines
% 0.73/1.10 ( Y, X ), unequally_directed_lines( X, Y ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 X := Y
% 0.73/1.10 Y := X
% 0.73/1.10 end
% 0.73/1.10 substitution1:
% 0.73/1.10 X := parallel_through_point( X, Y )
% 0.73/1.10 Y := X
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 subsumption: (122) {G2,W5,D3,L1,V2,M1} R(111,65) { !
% 0.73/1.10 unequally_directed_lines( X, parallel_through_point( X, Y ) ) }.
% 0.73/1.10 parent0: (973) {G1,W5,D3,L1,V2,M1} { ! unequally_directed_lines( X,
% 0.73/1.10 parallel_through_point( X, Y ) ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 X := X
% 0.73/1.10 Y := Y
% 0.73/1.10 end
% 0.73/1.10 permutation0:
% 0.73/1.10 0 ==> 0
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 resolution: (974) {G1,W8,D3,L2,V3,M2} { unequally_directed_lines( Z,
% 0.73/1.10 parallel_through_point( X, Y ) ), ! unequally_directed_lines( X, Z ) }.
% 0.73/1.10 parent0[0]: (122) {G2,W5,D3,L1,V2,M1} R(111,65) { !
% 0.73/1.10 unequally_directed_lines( X, parallel_through_point( X, Y ) ) }.
% 0.73/1.10 parent1[0]: (44) {G0,W9,D2,L3,V3,M3} I { unequally_directed_lines( X, Z ),
% 0.73/1.10 unequally_directed_lines( Y, Z ), ! unequally_directed_lines( X, Y ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 X := X
% 0.73/1.10 Y := Y
% 0.73/1.10 end
% 0.73/1.10 substitution1:
% 0.73/1.10 X := X
% 0.73/1.10 Y := Z
% 0.73/1.10 Z := parallel_through_point( X, Y )
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 subsumption: (124) {G3,W8,D3,L2,V3,M2} R(122,44) { !
% 0.73/1.10 unequally_directed_lines( Y, X ), unequally_directed_lines( X,
% 0.73/1.10 parallel_through_point( Y, Z ) ) }.
% 0.73/1.10 parent0: (974) {G1,W8,D3,L2,V3,M2} { unequally_directed_lines( Z,
% 0.73/1.10 parallel_through_point( X, Y ) ), ! unequally_directed_lines( X, Z ) }.
% 0.73/1.10 substitution0:
% 0.73/1.10 X := Y
% 0.73/1.10 Y := Z
% 0.73/1.10 Z := X
% 0.73/1.10 end
% 0.73/1.10 permutation0:
% 0.73/1.10 0 ==> 1
% 0.73/1.10 1 ==> 0
% 0.73/1.10 end
% 0.73/1.10
% 0.73/1.10 resolution: (976) {G1,W15,D3,L4,V3,M4} { ! alpha2( X, Y ), alpha7( X, Y, Z
% 0.73/1.10 ), unequally_directed_lines( X, line_connecting( Y, Z ) ), ! alpha5( X,
% 0.73/1.10 Z ) }.
% 0.73/1.10 parent0[2]: (20) {G0,W11,D2,L3,V3,M1} I { ! alpha2( X, Y ), alpha7( X, Y, Z
% 0.73/1.11 ), ! alpha8( X, Y, Z ) }.
% 0.73/1.11 parent1[2]: (23) {G0,W12,D3,L3,V3,M1} I { unequally_directed_lines( X,
% 0.73/1.11 line_connecting( Y, Z ) ), ! alpha5( X, Z ), alpha8( X, Y, Z ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Y
% 0.73/1.11 Z := Z
% 0.73/1.11 end
% 0.73/1.11 substitution1:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Y
% 0.73/1.11 Z := Z
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 subsumption: (131) {G1,W15,D3,L4,V3,M1} R(23,20) { unequally_directed_lines
% 0.73/1.11 ( X, line_connecting( Y, Z ) ), ! alpha2( X, Y ), ! alpha5( X, Z ),
% 0.73/1.11 alpha7( X, Y, Z ) }.
% 0.73/1.11 parent0: (976) {G1,W15,D3,L4,V3,M4} { ! alpha2( X, Y ), alpha7( X, Y, Z )
% 0.73/1.11 , unequally_directed_lines( X, line_connecting( Y, Z ) ), ! alpha5( X, Z
% 0.73/1.11 ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Y
% 0.73/1.11 Z := Z
% 0.73/1.11 end
% 0.73/1.11 permutation0:
% 0.73/1.11 0 ==> 1
% 0.73/1.11 1 ==> 3
% 0.73/1.11 2 ==> 0
% 0.73/1.11 3 ==> 2
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 resolution: (977) {G1,W7,D3,L2,V2,M2} { left_apart_point( X, reverse_line
% 0.73/1.11 ( Y ) ), alpha5( Y, X ) }.
% 0.73/1.11 parent0[0]: (52) {G0,W3,D2,L1,V2,M1} I { ! left_apart_point( X, Y ) }.
% 0.73/1.11 parent1[0]: (26) {G0,W10,D3,L3,V2,M1} I { left_apart_point( Y, X ),
% 0.73/1.11 left_apart_point( Y, reverse_line( X ) ), alpha5( X, Y ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Y
% 0.73/1.11 end
% 0.73/1.11 substitution1:
% 0.73/1.11 X := Y
% 0.73/1.11 Y := X
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 resolution: (979) {G1,W3,D2,L1,V2,M1} { alpha5( Y, X ) }.
% 0.73/1.11 parent0[0]: (52) {G0,W3,D2,L1,V2,M1} I { ! left_apart_point( X, Y ) }.
% 0.73/1.11 parent1[0]: (977) {G1,W7,D3,L2,V2,M2} { left_apart_point( X, reverse_line
% 0.73/1.11 ( Y ) ), alpha5( Y, X ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 Y := reverse_line( Y )
% 0.73/1.11 end
% 0.73/1.11 substitution1:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Y
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 subsumption: (153) {G1,W3,D2,L1,V2,M1} S(26);r(52);r(52) { alpha5( X, Y )
% 0.73/1.11 }.
% 0.73/1.11 parent0: (979) {G1,W3,D2,L1,V2,M1} { alpha5( Y, X ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := Y
% 0.73/1.11 Y := X
% 0.73/1.11 end
% 0.73/1.11 permutation0:
% 0.73/1.11 0 ==> 0
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 resolution: (980) {G1,W7,D3,L2,V2,M2} { left_apart_point( X, reverse_line
% 0.73/1.11 ( Y ) ), alpha2( Y, X ) }.
% 0.73/1.11 parent0[0]: (52) {G0,W3,D2,L1,V2,M1} I { ! left_apart_point( X, Y ) }.
% 0.73/1.11 parent1[0]: (29) {G0,W10,D3,L3,V2,M1} I { left_apart_point( Y, X ),
% 0.73/1.11 left_apart_point( Y, reverse_line( X ) ), alpha2( X, Y ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Y
% 0.73/1.11 end
% 0.73/1.11 substitution1:
% 0.73/1.11 X := Y
% 0.73/1.11 Y := X
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 resolution: (982) {G1,W3,D2,L1,V2,M1} { alpha2( Y, X ) }.
% 0.73/1.11 parent0[0]: (52) {G0,W3,D2,L1,V2,M1} I { ! left_apart_point( X, Y ) }.
% 0.73/1.11 parent1[0]: (980) {G1,W7,D3,L2,V2,M2} { left_apart_point( X, reverse_line
% 0.73/1.11 ( Y ) ), alpha2( Y, X ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 Y := reverse_line( Y )
% 0.73/1.11 end
% 0.73/1.11 substitution1:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Y
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 subsumption: (162) {G1,W3,D2,L1,V2,M1} S(29);r(52);r(52) { alpha2( X, Y )
% 0.73/1.11 }.
% 0.73/1.11 parent0: (982) {G1,W3,D2,L1,V2,M1} { alpha2( Y, X ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := Y
% 0.73/1.11 Y := X
% 0.73/1.11 end
% 0.73/1.11 permutation0:
% 0.73/1.11 0 ==> 0
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 resolution: (983) {G1,W6,D2,L2,V2,M2} { distinct_points( Y, X ), !
% 0.73/1.11 distinct_points( X, Y ) }.
% 0.73/1.11 parent0[0]: (39) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 0.73/1.11 parent1[0]: (40) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ),
% 0.73/1.11 distinct_points( Y, Z ), ! distinct_points( X, Y ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 end
% 0.73/1.11 substitution1:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Y
% 0.73/1.11 Z := X
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 subsumption: (288) {G1,W6,D2,L2,V2,M2} R(40,39) { ! distinct_points( Y, X )
% 0.73/1.11 , distinct_points( X, Y ) }.
% 0.73/1.11 parent0: (983) {G1,W6,D2,L2,V2,M2} { distinct_points( Y, X ), !
% 0.73/1.11 distinct_points( X, Y ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := Y
% 0.73/1.11 Y := X
% 0.73/1.11 end
% 0.73/1.11 permutation0:
% 0.73/1.11 0 ==> 1
% 0.73/1.11 1 ==> 0
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 resolution: (985) {G1,W3,D2,L1,V0,M1} { distinct_points( skol2, skol1 )
% 0.73/1.11 }.
% 0.73/1.11 parent0[0]: (288) {G1,W6,D2,L2,V2,M2} R(40,39) { ! distinct_points( Y, X )
% 0.73/1.11 , distinct_points( X, Y ) }.
% 0.73/1.11 parent1[0]: (67) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol1, skol2 )
% 0.73/1.11 }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := skol2
% 0.73/1.11 Y := skol1
% 0.73/1.11 end
% 0.73/1.11 substitution1:
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 subsumption: (291) {G2,W3,D2,L1,V0,M1} R(288,67) { distinct_points( skol2,
% 0.73/1.11 skol1 ) }.
% 0.73/1.11 parent0: (985) {G1,W3,D2,L1,V0,M1} { distinct_points( skol2, skol1 ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 end
% 0.73/1.11 permutation0:
% 0.73/1.11 0 ==> 0
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 resolution: (986) {G1,W10,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y
% 0.73/1.11 ), ! unequally_directed_lines( X, reverse_line( Y ) ),
% 0.73/1.11 left_convergent_lines( X, Y ) }.
% 0.73/1.11 parent0[0]: (53) {G0,W3,D2,L1,V2,M1} I { ! left_convergent_lines( X, Y )
% 0.73/1.11 }.
% 0.73/1.11 parent1[2]: (51) {G0,W14,D3,L4,V2,M2} I { ! unequally_directed_lines( X, Y
% 0.73/1.11 ), ! unequally_directed_lines( X, reverse_line( Y ) ),
% 0.73/1.11 left_convergent_lines( X, reverse_line( Y ) ), left_convergent_lines( X,
% 0.73/1.11 Y ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 Y := reverse_line( Y )
% 0.73/1.11 end
% 0.73/1.11 substitution1:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Y
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 resolution: (988) {G1,W7,D3,L2,V2,M2} { ! unequally_directed_lines( X, Y )
% 0.73/1.11 , ! unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.73/1.11 parent0[0]: (53) {G0,W3,D2,L1,V2,M1} I { ! left_convergent_lines( X, Y )
% 0.73/1.11 }.
% 0.73/1.11 parent1[2]: (986) {G1,W10,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y
% 0.73/1.11 ), ! unequally_directed_lines( X, reverse_line( Y ) ),
% 0.73/1.11 left_convergent_lines( X, Y ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Y
% 0.73/1.11 end
% 0.73/1.11 substitution1:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Y
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 subsumption: (401) {G1,W7,D3,L2,V2,M2} S(51);r(53);r(53) { !
% 0.73/1.11 unequally_directed_lines( X, reverse_line( Y ) ), !
% 0.73/1.11 unequally_directed_lines( X, Y ) }.
% 0.73/1.11 parent0: (988) {G1,W7,D3,L2,V2,M2} { ! unequally_directed_lines( X, Y ), !
% 0.73/1.11 unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Y
% 0.73/1.11 end
% 0.73/1.11 permutation0:
% 0.73/1.11 0 ==> 1
% 0.73/1.11 1 ==> 0
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 resolution: (990) {G2,W7,D3,L2,V2,M2} { ! unequally_directed_lines( X,
% 0.73/1.11 reverse_line( Y ) ), ! unequally_directed_lines( Y, X ) }.
% 0.73/1.11 parent0[1]: (401) {G1,W7,D3,L2,V2,M2} S(51);r(53);r(53) { !
% 0.73/1.11 unequally_directed_lines( X, reverse_line( Y ) ), !
% 0.73/1.11 unequally_directed_lines( X, Y ) }.
% 0.73/1.11 parent1[1]: (111) {G1,W6,D2,L2,V2,M2} R(44,43) { ! unequally_directed_lines
% 0.73/1.11 ( Y, X ), unequally_directed_lines( X, Y ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Y
% 0.73/1.11 end
% 0.73/1.11 substitution1:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Y
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 subsumption: (433) {G2,W7,D3,L2,V2,M2} R(401,111) { !
% 0.73/1.11 unequally_directed_lines( Y, X ), ! unequally_directed_lines( X,
% 0.73/1.11 reverse_line( Y ) ) }.
% 0.73/1.11 parent0: (990) {G2,W7,D3,L2,V2,M2} { ! unequally_directed_lines( X,
% 0.73/1.11 reverse_line( Y ) ), ! unequally_directed_lines( Y, X ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Y
% 0.73/1.11 end
% 0.73/1.11 permutation0:
% 0.73/1.11 0 ==> 1
% 0.73/1.11 1 ==> 0
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 resolution: (994) {G1,W10,D3,L3,V3,M3} { ! unequally_directed_lines( X, Y
% 0.73/1.11 ), unequally_directed_lines( Z, reverse_line( X ) ), !
% 0.73/1.11 unequally_directed_lines( Z, Y ) }.
% 0.73/1.11 parent0[1]: (433) {G2,W7,D3,L2,V2,M2} R(401,111) { !
% 0.73/1.11 unequally_directed_lines( Y, X ), ! unequally_directed_lines( X,
% 0.73/1.11 reverse_line( Y ) ) }.
% 0.73/1.11 parent1[1]: (44) {G0,W9,D2,L3,V3,M3} I { unequally_directed_lines( X, Z ),
% 0.73/1.11 unequally_directed_lines( Y, Z ), ! unequally_directed_lines( X, Y ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := Y
% 0.73/1.11 Y := X
% 0.73/1.11 end
% 0.73/1.11 substitution1:
% 0.73/1.11 X := Z
% 0.73/1.11 Y := Y
% 0.73/1.11 Z := reverse_line( X )
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 subsumption: (489) {G3,W10,D3,L3,V3,M3} R(433,44) {
% 0.73/1.11 unequally_directed_lines( Z, reverse_line( X ) ), !
% 0.73/1.11 unequally_directed_lines( Z, Y ), ! unequally_directed_lines( X, Y ) }.
% 0.73/1.11 parent0: (994) {G1,W10,D3,L3,V3,M3} { ! unequally_directed_lines( X, Y ),
% 0.73/1.11 unequally_directed_lines( Z, reverse_line( X ) ), !
% 0.73/1.11 unequally_directed_lines( Z, Y ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Y
% 0.73/1.11 Z := Z
% 0.73/1.11 end
% 0.73/1.11 permutation0:
% 0.73/1.11 0 ==> 2
% 0.73/1.11 1 ==> 0
% 0.73/1.11 2 ==> 1
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 factor: (998) {G3,W7,D3,L2,V2,M2} { unequally_directed_lines( X,
% 0.73/1.11 reverse_line( X ) ), ! unequally_directed_lines( X, Y ) }.
% 0.73/1.11 parent0[1, 2]: (489) {G3,W10,D3,L3,V3,M3} R(433,44) {
% 0.73/1.11 unequally_directed_lines( Z, reverse_line( X ) ), !
% 0.73/1.11 unequally_directed_lines( Z, Y ), ! unequally_directed_lines( X, Y ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Y
% 0.73/1.11 Z := X
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 subsumption: (490) {G4,W7,D3,L2,V2,M2} F(489) { ! unequally_directed_lines
% 0.73/1.11 ( X, Y ), unequally_directed_lines( X, reverse_line( X ) ) }.
% 0.73/1.11 parent0: (998) {G3,W7,D3,L2,V2,M2} { unequally_directed_lines( X,
% 0.73/1.11 reverse_line( X ) ), ! unequally_directed_lines( X, Y ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Y
% 0.73/1.11 end
% 0.73/1.11 permutation0:
% 0.73/1.11 0 ==> 1
% 0.73/1.11 1 ==> 0
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 resolution: (999) {G1,W5,D3,L1,V2,M1} { ! unequally_directed_lines(
% 0.73/1.11 line_connecting( X, X ), Y ) }.
% 0.73/1.11 parent0[0]: (64) {G0,W8,D4,L1,V2,M1} I { ! unequally_directed_lines(
% 0.73/1.11 line_connecting( X, Y ), reverse_line( line_connecting( Y, X ) ) ) }.
% 0.73/1.11 parent1[1]: (490) {G4,W7,D3,L2,V2,M2} F(489) { ! unequally_directed_lines(
% 0.73/1.11 X, Y ), unequally_directed_lines( X, reverse_line( X ) ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 Y := X
% 0.73/1.11 end
% 0.73/1.11 substitution1:
% 0.73/1.11 X := line_connecting( X, X )
% 0.73/1.11 Y := Y
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 subsumption: (510) {G5,W5,D3,L1,V2,M1} R(490,64) { !
% 0.73/1.11 unequally_directed_lines( line_connecting( X, X ), Y ) }.
% 0.73/1.11 parent0: (999) {G1,W5,D3,L1,V2,M1} { ! unequally_directed_lines(
% 0.73/1.11 line_connecting( X, X ), Y ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Y
% 0.73/1.11 end
% 0.73/1.11 permutation0:
% 0.73/1.11 0 ==> 0
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 resolution: (1000) {G4,W5,D3,L1,V2,M1} { ! unequally_directed_lines( Y,
% 0.73/1.11 line_connecting( X, X ) ) }.
% 0.73/1.11 parent0[0]: (510) {G5,W5,D3,L1,V2,M1} R(490,64) { !
% 0.73/1.11 unequally_directed_lines( line_connecting( X, X ), Y ) }.
% 0.73/1.11 parent1[1]: (124) {G3,W8,D3,L2,V3,M2} R(122,44) { !
% 0.73/1.11 unequally_directed_lines( Y, X ), unequally_directed_lines( X,
% 0.73/1.11 parallel_through_point( Y, Z ) ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 Y := parallel_through_point( Y, Z )
% 0.73/1.11 end
% 0.73/1.11 substitution1:
% 0.73/1.11 X := line_connecting( X, X )
% 0.73/1.11 Y := Y
% 0.73/1.11 Z := Z
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 subsumption: (515) {G6,W5,D3,L1,V2,M1} R(510,124) { !
% 0.73/1.11 unequally_directed_lines( X, line_connecting( Y, Y ) ) }.
% 0.73/1.11 parent0: (1000) {G4,W5,D3,L1,V2,M1} { ! unequally_directed_lines( Y,
% 0.73/1.11 line_connecting( X, X ) ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := Y
% 0.73/1.11 Y := X
% 0.73/1.11 end
% 0.73/1.11 permutation0:
% 0.73/1.11 0 ==> 0
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 resolution: (1001) {G1,W8,D3,L2,V3,M2} { unequally_directed_lines( Z,
% 0.73/1.11 line_connecting( Y, Y ) ), ! unequally_directed_lines( X, Z ) }.
% 0.73/1.11 parent0[0]: (515) {G6,W5,D3,L1,V2,M1} R(510,124) { !
% 0.73/1.11 unequally_directed_lines( X, line_connecting( Y, Y ) ) }.
% 0.73/1.11 parent1[0]: (44) {G0,W9,D2,L3,V3,M3} I { unequally_directed_lines( X, Z ),
% 0.73/1.11 unequally_directed_lines( Y, Z ), ! unequally_directed_lines( X, Y ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Y
% 0.73/1.11 end
% 0.73/1.11 substitution1:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Z
% 0.73/1.11 Z := line_connecting( Y, Y )
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 resolution: (1003) {G2,W3,D2,L1,V2,M1} { ! unequally_directed_lines( Z, X
% 0.73/1.11 ) }.
% 0.73/1.11 parent0[0]: (515) {G6,W5,D3,L1,V2,M1} R(510,124) { !
% 0.73/1.11 unequally_directed_lines( X, line_connecting( Y, Y ) ) }.
% 0.73/1.11 parent1[0]: (1001) {G1,W8,D3,L2,V3,M2} { unequally_directed_lines( Z,
% 0.73/1.11 line_connecting( Y, Y ) ), ! unequally_directed_lines( X, Z ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Y
% 0.73/1.11 end
% 0.73/1.11 substitution1:
% 0.73/1.11 X := Z
% 0.73/1.11 Y := Y
% 0.73/1.11 Z := X
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 subsumption: (516) {G7,W3,D2,L1,V2,M1} R(515,44);r(515) { !
% 0.73/1.11 unequally_directed_lines( Z, X ) }.
% 0.73/1.11 parent0: (1003) {G2,W3,D2,L1,V2,M1} { ! unequally_directed_lines( Z, X )
% 0.73/1.11 }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 Y := T
% 0.73/1.11 Z := Z
% 0.73/1.11 end
% 0.73/1.11 permutation0:
% 0.73/1.11 0 ==> 0
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 resolution: (1004) {G3,W8,D2,L2,V0,M2} { ! alpha7( skol3, skol2, skol1 ),
% 0.73/1.11 ! alpha7( skol3, skol1, skol2 ) }.
% 0.73/1.11 parent0[0]: (97) {G2,W11,D2,L3,V0,M1} R(96,17) { ! distinct_points( skol2,
% 0.73/1.11 skol1 ), ! alpha7( skol3, skol2, skol1 ), ! alpha7( skol3, skol1, skol2 )
% 0.73/1.11 }.
% 0.73/1.11 parent1[0]: (291) {G2,W3,D2,L1,V0,M1} R(288,67) { distinct_points( skol2,
% 0.73/1.11 skol1 ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 end
% 0.73/1.11 substitution1:
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 subsumption: (666) {G3,W8,D2,L2,V0,M1} S(97);r(291) { ! alpha7( skol3,
% 0.73/1.11 skol2, skol1 ), ! alpha7( skol3, skol1, skol2 ) }.
% 0.73/1.11 parent0: (1004) {G3,W8,D2,L2,V0,M2} { ! alpha7( skol3, skol2, skol1 ), !
% 0.73/1.11 alpha7( skol3, skol1, skol2 ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 end
% 0.73/1.11 permutation0:
% 0.73/1.11 0 ==> 0
% 0.73/1.11 1 ==> 1
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 resolution: (1005) {G2,W10,D2,L3,V3,M3} { ! alpha2( X, Y ), ! alpha5( X, Z
% 0.73/1.11 ), alpha7( X, Y, Z ) }.
% 0.73/1.11 parent0[0]: (516) {G7,W3,D2,L1,V2,M1} R(515,44);r(515) { !
% 0.73/1.11 unequally_directed_lines( Z, X ) }.
% 0.73/1.11 parent1[0]: (131) {G1,W15,D3,L4,V3,M1} R(23,20) { unequally_directed_lines
% 0.73/1.11 ( X, line_connecting( Y, Z ) ), ! alpha2( X, Y ), ! alpha5( X, Z ),
% 0.73/1.11 alpha7( X, Y, Z ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := line_connecting( Y, Z )
% 0.73/1.11 Y := T
% 0.73/1.11 Z := X
% 0.73/1.11 end
% 0.73/1.11 substitution1:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Y
% 0.73/1.11 Z := Z
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 resolution: (1006) {G2,W7,D2,L2,V3,M2} { ! alpha5( X, Z ), alpha7( X, Y, Z
% 0.73/1.11 ) }.
% 0.73/1.11 parent0[0]: (1005) {G2,W10,D2,L3,V3,M3} { ! alpha2( X, Y ), ! alpha5( X, Z
% 0.73/1.11 ), alpha7( X, Y, Z ) }.
% 0.73/1.11 parent1[0]: (162) {G1,W3,D2,L1,V2,M1} S(29);r(52);r(52) { alpha2( X, Y )
% 0.73/1.11 }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Y
% 0.73/1.11 Z := Z
% 0.73/1.11 end
% 0.73/1.11 substitution1:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Y
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 resolution: (1007) {G2,W4,D2,L1,V3,M1} { alpha7( X, Z, Y ) }.
% 0.73/1.11 parent0[0]: (1006) {G2,W7,D2,L2,V3,M2} { ! alpha5( X, Z ), alpha7( X, Y, Z
% 0.73/1.11 ) }.
% 0.73/1.11 parent1[0]: (153) {G1,W3,D2,L1,V2,M1} S(26);r(52);r(52) { alpha5( X, Y )
% 0.73/1.11 }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Z
% 0.73/1.11 Z := Y
% 0.73/1.11 end
% 0.73/1.11 substitution1:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Y
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 subsumption: (771) {G8,W4,D2,L1,V3,M1} S(131);r(516);r(162);r(153) { alpha7
% 0.73/1.11 ( X, Y, Z ) }.
% 0.73/1.11 parent0: (1007) {G2,W4,D2,L1,V3,M1} { alpha7( X, Z, Y ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 X := X
% 0.73/1.11 Y := Z
% 0.73/1.11 Z := Y
% 0.73/1.11 end
% 0.73/1.11 permutation0:
% 0.73/1.11 0 ==> 0
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 resolution: (1008) {G4,W4,D2,L1,V0,M1} { ! alpha7( skol3, skol1, skol2 )
% 0.73/1.11 }.
% 0.73/1.11 parent0[0]: (666) {G3,W8,D2,L2,V0,M1} S(97);r(291) { ! alpha7( skol3, skol2
% 0.73/1.11 , skol1 ), ! alpha7( skol3, skol1, skol2 ) }.
% 0.73/1.11 parent1[0]: (771) {G8,W4,D2,L1,V3,M1} S(131);r(516);r(162);r(153) { alpha7
% 0.73/1.11 ( X, Y, Z ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 end
% 0.73/1.11 substitution1:
% 0.73/1.11 X := skol3
% 0.73/1.11 Y := skol2
% 0.73/1.11 Z := skol1
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 resolution: (1010) {G5,W0,D0,L0,V0,M0} { }.
% 0.73/1.11 parent0[0]: (1008) {G4,W4,D2,L1,V0,M1} { ! alpha7( skol3, skol1, skol2 )
% 0.73/1.11 }.
% 0.73/1.11 parent1[0]: (771) {G8,W4,D2,L1,V3,M1} S(131);r(516);r(162);r(153) { alpha7
% 0.73/1.11 ( X, Y, Z ) }.
% 0.73/1.11 substitution0:
% 0.73/1.11 end
% 0.73/1.11 substitution1:
% 0.73/1.11 X := skol3
% 0.73/1.11 Y := skol1
% 0.73/1.11 Z := skol2
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 subsumption: (772) {G9,W0,D0,L0,V0,M0} R(771,666);r(771) { }.
% 0.73/1.11 parent0: (1010) {G5,W0,D0,L0,V0,M0} { }.
% 0.73/1.11 substitution0:
% 0.73/1.11 end
% 0.73/1.11 permutation0:
% 0.73/1.11 end
% 0.73/1.11
% 0.73/1.11 Proof check complete!
% 0.73/1.11
% 0.73/1.11 Memory use:
% 0.73/1.11
% 0.73/1.11 space for terms: 10484
% 0.73/1.11 space for clauses: 35190
% 0.73/1.11
% 0.73/1.11
% 0.73/1.11 clauses generated: 3597
% 0.73/1.11 clauses kept: 773
% 0.73/1.11 clauses selected: 174
% 0.73/1.11 clauses deleted: 128
% 0.73/1.11 clauses inuse deleted: 0
% 0.73/1.11
% 0.73/1.11 subsentry: 45543
% 0.73/1.11 literals s-matched: 21900
% 0.73/1.11 literals matched: 21797
% 0.73/1.11 full subsumption: 7735
% 0.73/1.11
% 0.73/1.11 checksum: 1607977237
% 0.73/1.11
% 0.73/1.11
% 0.73/1.11 Bliksem ended
%------------------------------------------------------------------------------