%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO231+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n003.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 02:53:05 EDT 2022
% Result : Theorem 0.42s 1.07s
% Output : Refutation 0.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : GEO231+3 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n003.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 : Fri Jun 17 18:49:12 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 { ! unequally_directed_opposite_lines( X, Y ), unequally_directed_lines( X
% 0.42/1.06 , reverse_line( Y ) ) }.
% 0.42/1.06 { ! unequally_directed_lines( X, reverse_line( Y ) ),
% 0.42/1.06 unequally_directed_opposite_lines( X, Y ) }.
% 0.42/1.06 { ! right_apart_point( X, Y ), left_apart_point( X, reverse_line( Y ) ) }.
% 0.42/1.06 { ! left_apart_point( X, reverse_line( Y ) ), right_apart_point( X, Y ) }.
% 0.42/1.06 { ! right_convergent_lines( X, Y ), left_convergent_lines( X, reverse_line
% 0.42/1.06 ( Y ) ) }.
% 0.42/1.06 { ! left_convergent_lines( X, reverse_line( Y ) ), right_convergent_lines(
% 0.42/1.06 X, Y ) }.
% 0.42/1.06 { ! equally_directed_lines( X, Y ), ! unequally_directed_lines( X, Y ) }.
% 0.42/1.06 { unequally_directed_lines( X, Y ), equally_directed_lines( X, Y ) }.
% 0.42/1.06 { ! equally_directed_opposite_lines( X, Y ), !
% 0.42/1.06 unequally_directed_opposite_lines( X, Y ) }.
% 0.42/1.06 { unequally_directed_opposite_lines( X, Y ),
% 0.42/1.06 equally_directed_opposite_lines( X, Y ) }.
% 0.42/1.06 { ! apart_point_and_line( X, Y ), left_apart_point( X, Y ),
% 0.42/1.06 right_apart_point( X, Y ) }.
% 0.42/1.06 { ! left_apart_point( X, Y ), apart_point_and_line( X, Y ) }.
% 0.42/1.06 { ! right_apart_point( X, Y ), apart_point_and_line( X, Y ) }.
% 0.42/1.06 { ! convergent_lines( X, Y ), unequally_directed_lines( X, Y ) }.
% 0.42/1.06 { ! convergent_lines( X, Y ), unequally_directed_opposite_lines( X, Y ) }.
% 0.42/1.06 { ! unequally_directed_lines( X, Y ), ! unequally_directed_opposite_lines(
% 0.42/1.06 X, 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 ), right_apart_point( X, Z ) }.
% 0.42/1.06 { ! alpha4( X, Y, Z ), left_apart_point( Y, Z ) }.
% 0.42/1.06 { ! right_apart_point( X, Z ), ! left_apart_point( Y, Z ), alpha4( X, Y, Z
% 0.42/1.06 ) }.
% 0.42/1.06 { ! alpha1( X, Y, Z ), left_apart_point( X, Z ) }.
% 0.42/1.06 { ! alpha1( X, Y, Z ), right_apart_point( Y, Z ) }.
% 0.42/1.06 { ! left_apart_point( X, Z ), ! right_apart_point( Y, Z ), alpha1( X, Y, Z
% 0.42/1.06 ) }.
% 0.42/1.06 { ! before_on_line( X, Y, Z ), distinct_points( Y, Z ) }.
% 0.42/1.06 { ! before_on_line( X, Y, Z ), alpha2( X, Y, Z ) }.
% 0.42/1.06 { ! distinct_points( Y, Z ), ! alpha2( X, Y, Z ), before_on_line( X, Y, Z )
% 0.42/1.06 }.
% 0.42/1.06 { ! alpha2( X, Y, Z ), incident_point_and_line( Y, X ) }.
% 0.42/1.06 { ! alpha2( X, Y, Z ), alpha5( X, Y, Z ) }.
% 0.42/1.06 { ! incident_point_and_line( Y, X ), ! alpha5( X, Y, Z ), alpha2( X, Y, Z )
% 0.42/1.06 }.
% 0.42/1.06 { ! alpha5( X, Y, Z ), incident_point_and_line( Z, X ) }.
% 0.42/1.06 { ! alpha5( X, Y, Z ), equally_directed_lines( X, line_connecting( Y, Z ) )
% 0.42/1.06 }.
% 0.42/1.06 { ! incident_point_and_line( Z, X ), ! equally_directed_lines( X,
% 0.42/1.06 line_connecting( Y, Z ) ), alpha5( X, Y, Z ) }.
% 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 { equally_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 ) ), alpha7( 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 ) ), alpha7( X, Z ), unequally_directed_lines( Y,
% 0.42/1.06 reverse_line( Z ) ) }.
% 0.42/1.06 { ! alpha7( X, Y ), unequally_directed_lines( X, Y ) }.
% 0.42/1.06 { ! alpha7( X, Y ), unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.42/1.07 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.42/1.07 reverse_line( Y ) ), alpha7( X, Y ) }.
% 0.42/1.07 { unequally_directed_lines( X, Y ), unequally_directed_lines( X,
% 0.42/1.07 reverse_line( Y ) ) }.
% 0.42/1.07 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.42/1.07 reverse_line( Y ) ), left_convergent_lines( X, Y ), left_convergent_lines
% 0.42/1.07 ( X, reverse_line( Y ) ) }.
% 0.42/1.07 { ! left_apart_point( X, Y ) }.
% 0.42/1.07 { ! left_apart_point( X, reverse_line( Y ) ) }.
% 0.42/1.07 { ! left_convergent_lines( X, Y ) }.
% 0.42/1.07 { ! left_convergent_lines( X, reverse_line( Y ) ) }.
% 0.42/1.07 { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line(
% 0.42/1.07 line_connecting( X, Y ) ) }.
% 0.42/1.07 { ! line( X ), ! line( Y ), ! unequally_directed_lines( X, Y ), !
% 0.42/1.07 unequally_directed_lines( X, reverse_line( Y ) ), point(
% 0.42/1.07 intersection_point( X, Y ) ) }.
% 0.42/1.07 { ! point( Y ), ! line( X ), line( parallel_through_point( X, Y ) ) }.
% 0.42/1.07 { ! line( X ), line( reverse_line( X ) ) }.
% 0.42/1.07 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 0.42/1.07 , Y ) ) }.
% 0.42/1.07 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 0.42/1.07 , Y ) ) }.
% 0.42/1.07 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.42/1.07 reverse_line( Y ) ), ! apart_point_and_line( intersection_point( X, Y ),
% 0.42/1.07 X ) }.
% 0.42/1.07 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.42/1.07 reverse_line( Y ) ), ! apart_point_and_line( intersection_point( X, Y ),
% 0.42/1.07 Y ) }.
% 0.42/1.07 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 0.42/1.07 { ! distinct_lines( X, reverse_line( X ) ) }.
% 0.42/1.07 { ! distinct_points( X, Y ), equally_directed_lines( line_connecting( X, Y
% 0.42/1.07 ), reverse_line( line_connecting( Y, X ) ) ) }.
% 0.42/1.07 { equally_directed_lines( parallel_through_point( Y, X ), Y ) }.
% 0.42/1.07 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), left_apart_point( X
% 0.42/1.07 , Z ), left_apart_point( Y, Z ), left_apart_point( X, T ),
% 0.42/1.07 left_apart_point( Y, T ), left_apart_point( X, reverse_line( Z ) ),
% 0.42/1.07 left_apart_point( Y, reverse_line( Z ) ), left_apart_point( X,
% 0.42/1.07 reverse_line( T ) ), left_apart_point( Y, reverse_line( T ) ) }.
% 0.42/1.07 { ! distinct_points( X, Y ), ! left_apart_point( X, Z ), left_apart_point(
% 0.42/1.07 Y, Z ), left_convergent_lines( line_connecting( X, Y ), Z ) }.
% 0.42/1.07 { ! left_apart_point( X, Y ), distinct_points( X, Z ), left_apart_point( Z
% 0.42/1.07 , Y ) }.
% 0.42/1.07 { ! left_apart_point( X, Y ), ! unequally_directed_lines( Y, Z ),
% 0.42/1.07 distinct_lines( Y, Z ), left_apart_point( X, reverse_line( Z ) ) }.
% 0.42/1.07 { ! left_convergent_lines( X, Y ), unequally_directed_lines( Y, Z ),
% 0.42/1.07 left_convergent_lines( X, Z ) }.
% 0.42/1.07 { equally_directed_opposite_lines( skol3, skol1 ) }.
% 0.42/1.07 { equally_directed_lines( skol3, skol2 ) }.
% 0.42/1.07 { ! equally_directed_opposite_lines( skol1, skol2 ) }.
% 0.42/1.07
% 0.42/1.07 percentage equality = 0.000000, percentage horn = 0.824324
% 0.42/1.07 This a non-horn, non-equality problem
% 0.42/1.07
% 0.42/1.07
% 0.42/1.07 Options Used:
% 0.42/1.07
% 0.42/1.07 useres = 1
% 0.42/1.07 useparamod = 0
% 0.42/1.07 useeqrefl = 0
% 0.42/1.07 useeqfact = 0
% 0.42/1.07 usefactor = 1
% 0.42/1.07 usesimpsplitting = 0
% 0.42/1.07 usesimpdemod = 0
% 0.42/1.07 usesimpres = 3
% 0.42/1.07
% 0.42/1.07 resimpinuse = 1000
% 0.42/1.07 resimpclauses = 20000
% 0.42/1.07 substype = standard
% 0.42/1.07 backwardsubs = 1
% 0.42/1.07 selectoldest = 5
% 0.42/1.07
% 0.42/1.07 litorderings [0] = split
% 0.42/1.07 litorderings [1] = liftord
% 0.42/1.07
% 0.42/1.07 termordering = none
% 0.42/1.07
% 0.42/1.07 litapriori = 1
% 0.42/1.07 termapriori = 0
% 0.42/1.07 litaposteriori = 0
% 0.42/1.07 termaposteriori = 0
% 0.42/1.07 demodaposteriori = 0
% 0.42/1.07 ordereqreflfact = 0
% 0.42/1.07
% 0.42/1.07 litselect = none
% 0.42/1.07
% 0.42/1.07 maxweight = 15
% 0.42/1.07 maxdepth = 30000
% 0.42/1.07 maxlength = 115
% 0.42/1.07 maxnrvars = 195
% 0.42/1.07 excuselevel = 1
% 0.42/1.07 increasemaxweight = 1
% 0.42/1.07
% 0.42/1.07 maxselected = 10000000
% 0.42/1.07 maxnrclauses = 10000000
% 0.42/1.07
% 0.42/1.07 showgenerated = 0
% 0.42/1.07 showkept = 0
% 0.42/1.07 showselected = 0
% 0.42/1.07 showdeleted = 0
% 0.42/1.07 showresimp = 1
% 0.42/1.07 showstatus = 2000
% 0.42/1.07
% 0.42/1.07 prologoutput = 0
% 0.42/1.07 nrgoals = 5000000
% 0.42/1.07 totalproof = 1
% 0.42/1.07
% 0.42/1.07 Symbols occurring in the translation:
% 0.42/1.07
% 0.42/1.07 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.42/1.07 . [1, 2] (w:1, o:25, a:1, s:1, b:0),
% 0.42/1.07 ! [4, 1] (w:0, o:17, a:1, s:1, b:0),
% 0.42/1.07 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.42/1.07 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.42/1.07 unequally_directed_opposite_lines [37, 2] (w:1, o:49, a:1, s:1, b:0)
% 0.42/1.07 ,
% 0.42/1.07 reverse_line [38, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.42/1.07 unequally_directed_lines [39, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.42/1.07 right_apart_point [40, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.42/1.07 left_apart_point [41, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.42/1.07 right_convergent_lines [42, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.42/1.07 left_convergent_lines [43, 2] (w:1, o:54, a:1, s:1, b:0),
% 0.42/1.07 equally_directed_lines [44, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.42/1.07 equally_directed_opposite_lines [45, 2] (w:1, o:58, a:1, s:1, b:0),
% 0.42/1.07 apart_point_and_line [48, 2] (w:1, o:59, a:1, s:1, b:0),
% 0.42/1.07 convergent_lines [50, 2] (w:1, o:60, a:1, s:1, b:0),
% 0.42/1.07 divides_points [52, 3] (w:1, o:66, a:1, s:1, b:0),
% 0.42/1.07 before_on_line [53, 3] (w:1, o:71, a:1, s:1, b:0),
% 0.42/1.07 distinct_points [54, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.42/1.07 incident_point_and_line [55, 2] (w:1, o:61, a:1, s:1, b:0),
% 0.42/1.07 line_connecting [56, 2] (w:1, o:62, a:1, s:1, b:0),
% 0.42/1.07 between_on_line [58, 4] (w:1, o:74, a:1, s:1, b:0),
% 0.42/1.07 distinct_lines [59, 2] (w:1, o:56, a:1, s:1, b:0),
% 0.42/1.07 point [61, 1] (w:1, o:23, a:1, s:1, b:0),
% 0.42/1.07 line [62, 1] (w:1, o:24, a:1, s:1, b:0),
% 0.42/1.07 intersection_point [63, 2] (w:1, o:63, a:1, s:1, b:0),
% 0.42/1.07 parallel_through_point [64, 2] (w:1, o:64, a:1, s:1, b:0),
% 0.42/1.07 alpha1 [65, 3] (w:1, o:67, a:1, s:1, b:0),
% 0.42/1.07 alpha2 [66, 3] (w:1, o:68, a:1, s:1, b:0),
% 0.42/1.07 alpha3 [67, 4] (w:1, o:72, a:1, s:1, b:0),
% 0.42/1.07 alpha4 [68, 3] (w:1, o:69, a:1, s:1, b:0),
% 0.42/1.07 alpha5 [69, 3] (w:1, o:70, a:1, s:1, b:0),
% 0.42/1.07 alpha6 [70, 4] (w:1, o:73, a:1, s:1, b:0),
% 0.42/1.07 alpha7 [71, 2] (w:1, o:65, a:1, s:1, b:0),
% 0.42/1.07 skol1 [72, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.42/1.07 skol2 [73, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.42/1.07 skol3 [74, 0] (w:1, o:16, a:1, s:1, b:0).
% 0.42/1.07
% 0.42/1.07
% 0.42/1.07 Starting Search:
% 0.42/1.07
% 0.42/1.07 *** allocated 15000 integers for clauses
% 0.42/1.07 *** allocated 22500 integers for clauses
% 0.42/1.07 *** allocated 33750 integers for clauses
% 0.42/1.07
% 0.42/1.07 Bliksems!, er is een bewijs:
% 0.42/1.07 % SZS status Theorem
% 0.42/1.07 % SZS output start Refutation
% 0.42/1.07
% 0.42/1.07 (0) {G0,W7,D3,L2,V2,M1} I { ! unequally_directed_opposite_lines( X, Y ),
% 0.42/1.07 unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.42/1.07 (1) {G0,W7,D3,L2,V2,M1} I { unequally_directed_opposite_lines( X, Y ), !
% 0.42/1.07 unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.42/1.07 (6) {G0,W6,D2,L2,V2,M1} I { ! unequally_directed_lines( X, Y ), !
% 0.42/1.07 equally_directed_lines( X, Y ) }.
% 0.42/1.07 (8) {G0,W6,D2,L2,V2,M1} I { ! unequally_directed_opposite_lines( X, Y ), !
% 0.42/1.07 equally_directed_opposite_lines( X, Y ) }.
% 0.42/1.07 (9) {G0,W6,D2,L2,V2,M1} I { unequally_directed_opposite_lines( X, Y ),
% 0.42/1.07 equally_directed_opposite_lines( X, Y ) }.
% 0.42/1.07 (48) {G0,W9,D2,L3,V3,M3} I { unequally_directed_lines( X, Z ),
% 0.42/1.07 unequally_directed_lines( Y, Z ), ! unequally_directed_lines( X, Y ) }.
% 0.42/1.07 (54) {G0,W7,D3,L2,V2,M2} I { unequally_directed_lines( X, reverse_line( Y )
% 0.42/1.07 ), unequally_directed_lines( X, Y ) }.
% 0.42/1.07 (55) {G0,W14,D3,L4,V2,M2} I { ! unequally_directed_lines( X, Y ), !
% 0.42/1.07 unequally_directed_lines( X, reverse_line( Y ) ), left_convergent_lines(
% 0.42/1.07 X, reverse_line( Y ) ), left_convergent_lines( X, Y ) }.
% 0.42/1.07 (57) {G0,W3,D2,L1,V2,M1} I { ! left_convergent_lines( X, Y ) }.
% 0.42/1.07 (71) {G0,W3,D2,L1,V0,M1} I { equally_directed_opposite_lines( skol3, skol1
% 0.42/1.07 ) }.
% 0.42/1.07 (72) {G0,W3,D2,L1,V0,M1} I { equally_directed_lines( skol3, skol2 ) }.
% 0.42/1.07 (73) {G0,W3,D2,L1,V0,M1} I { ! equally_directed_opposite_lines( skol1,
% 0.42/1.07 skol2 ) }.
% 0.42/1.07 (83) {G1,W3,D2,L1,V0,M1} R(9,73) { unequally_directed_opposite_lines( skol1
% 0.42/1.07 , skol2 ) }.
% 0.42/1.07 (85) {G1,W3,D2,L1,V0,M1} R(8,71) { ! unequally_directed_opposite_lines(
% 0.42/1.07 skol3, skol1 ) }.
% 0.42/1.07 (87) {G1,W3,D2,L1,V0,M1} R(6,72) { ! unequally_directed_lines( skol3, skol2
% 0.42/1.07 ) }.
% 0.42/1.07 (102) {G1,W6,D2,L2,V2,M1} R(54,1) { unequally_directed_opposite_lines( X, Y
% 0.42/1.07 ), unequally_directed_lines( X, Y ) }.
% 0.42/1.07 (141) {G2,W6,D2,L2,V1,M2} R(48,87) { ! unequally_directed_lines( skol3, X )
% 0.42/1.07 , unequally_directed_lines( X, skol2 ) }.
% 0.42/1.07 (216) {G3,W6,D2,L2,V1,M1} R(141,102) { unequally_directed_opposite_lines(
% 0.42/1.07 skol3, X ), unequally_directed_lines( X, skol2 ) }.
% 0.42/1.07 (267) {G1,W7,D3,L2,V2,M2} S(55);r(57);r(57) { ! unequally_directed_lines( X
% 0.42/1.07 , reverse_line( Y ) ), ! unequally_directed_lines( X, Y ) }.
% 0.42/1.07 (338) {G2,W6,D2,L2,V2,M1} R(267,0) { ! unequally_directed_opposite_lines( X
% 0.42/1.07 , Y ), ! unequally_directed_lines( X, Y ) }.
% 0.42/1.07 (400) {G4,W6,D2,L2,V1,M2} R(338,216) { unequally_directed_opposite_lines(
% 0.42/1.07 skol3, X ), ! unequally_directed_opposite_lines( X, skol2 ) }.
% 0.42/1.07 (463) {G5,W0,D0,L0,V0,M0} R(400,85);r(83) { }.
% 0.42/1.07
% 0.42/1.07
% 0.42/1.07 % SZS output end Refutation
% 0.42/1.07 found a proof!
% 0.42/1.07
% 0.42/1.07
% 0.42/1.07 Unprocessed initial clauses:
% 0.42/1.07
% 0.42/1.07 (465) {G0,W7,D3,L2,V2,M2} { ! unequally_directed_opposite_lines( X, Y ),
% 0.42/1.07 unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.42/1.07 (466) {G0,W7,D3,L2,V2,M2} { ! unequally_directed_lines( X, reverse_line( Y
% 0.42/1.07 ) ), unequally_directed_opposite_lines( X, Y ) }.
% 0.42/1.07 (467) {G0,W7,D3,L2,V2,M2} { ! right_apart_point( X, Y ), left_apart_point
% 0.42/1.07 ( X, reverse_line( Y ) ) }.
% 0.42/1.07 (468) {G0,W7,D3,L2,V2,M2} { ! left_apart_point( X, reverse_line( Y ) ),
% 0.42/1.07 right_apart_point( X, Y ) }.
% 0.42/1.07 (469) {G0,W7,D3,L2,V2,M2} { ! right_convergent_lines( X, Y ),
% 0.42/1.07 left_convergent_lines( X, reverse_line( Y ) ) }.
% 0.42/1.07 (470) {G0,W7,D3,L2,V2,M2} { ! left_convergent_lines( X, reverse_line( Y )
% 0.42/1.07 ), right_convergent_lines( X, Y ) }.
% 0.42/1.07 (471) {G0,W6,D2,L2,V2,M2} { ! equally_directed_lines( X, Y ), !
% 0.42/1.07 unequally_directed_lines( X, Y ) }.
% 0.42/1.07 (472) {G0,W6,D2,L2,V2,M2} { unequally_directed_lines( X, Y ),
% 0.42/1.07 equally_directed_lines( X, Y ) }.
% 0.42/1.07 (473) {G0,W6,D2,L2,V2,M2} { ! equally_directed_opposite_lines( X, Y ), !
% 0.42/1.07 unequally_directed_opposite_lines( X, Y ) }.
% 0.42/1.07 (474) {G0,W6,D2,L2,V2,M2} { unequally_directed_opposite_lines( X, Y ),
% 0.42/1.07 equally_directed_opposite_lines( X, Y ) }.
% 0.42/1.07 (475) {G0,W9,D2,L3,V2,M3} { ! apart_point_and_line( X, Y ),
% 0.42/1.07 left_apart_point( X, Y ), right_apart_point( X, Y ) }.
% 0.42/1.07 (476) {G0,W6,D2,L2,V2,M2} { ! left_apart_point( X, Y ),
% 0.42/1.07 apart_point_and_line( X, Y ) }.
% 0.42/1.07 (477) {G0,W6,D2,L2,V2,M2} { ! right_apart_point( X, Y ),
% 0.42/1.07 apart_point_and_line( X, Y ) }.
% 0.42/1.07 (478) {G0,W6,D2,L2,V2,M2} { ! convergent_lines( X, Y ),
% 0.42/1.07 unequally_directed_lines( X, Y ) }.
% 0.42/1.07 (479) {G0,W6,D2,L2,V2,M2} { ! convergent_lines( X, Y ),
% 0.42/1.07 unequally_directed_opposite_lines( X, Y ) }.
% 0.42/1.07 (480) {G0,W9,D2,L3,V2,M3} { ! unequally_directed_lines( X, Y ), !
% 0.42/1.07 unequally_directed_opposite_lines( X, Y ), convergent_lines( X, Y ) }.
% 0.42/1.07 (481) {G0,W12,D2,L3,V3,M3} { ! divides_points( Z, X, Y ), alpha1( X, Y, Z
% 0.42/1.07 ), alpha4( X, Y, Z ) }.
% 0.42/1.07 (482) {G0,W8,D2,L2,V3,M2} { ! alpha1( X, Y, Z ), divides_points( Z, X, Y )
% 0.42/1.07 }.
% 0.42/1.07 (483) {G0,W8,D2,L2,V3,M2} { ! alpha4( X, Y, Z ), divides_points( Z, X, Y )
% 0.42/1.07 }.
% 0.42/1.07 (484) {G0,W7,D2,L2,V3,M2} { ! alpha4( X, Y, Z ), right_apart_point( X, Z )
% 0.42/1.07 }.
% 0.42/1.07 (485) {G0,W7,D2,L2,V3,M2} { ! alpha4( X, Y, Z ), left_apart_point( Y, Z )
% 0.42/1.07 }.
% 0.42/1.07 (486) {G0,W10,D2,L3,V3,M3} { ! right_apart_point( X, Z ), !
% 0.42/1.07 left_apart_point( Y, Z ), alpha4( X, Y, Z ) }.
% 0.42/1.07 (487) {G0,W7,D2,L2,V3,M2} { ! alpha1( X, Y, Z ), left_apart_point( X, Z )
% 0.42/1.07 }.
% 0.42/1.07 (488) {G0,W7,D2,L2,V3,M2} { ! alpha1( X, Y, Z ), right_apart_point( Y, Z )
% 0.42/1.07 }.
% 0.42/1.07 (489) {G0,W10,D2,L3,V3,M3} { ! left_apart_point( X, Z ), !
% 0.42/1.07 right_apart_point( Y, Z ), alpha1( X, Y, Z ) }.
% 0.42/1.07 (490) {G0,W7,D2,L2,V3,M2} { ! before_on_line( X, Y, Z ), distinct_points(
% 0.42/1.07 Y, Z ) }.
% 0.42/1.07 (491) {G0,W8,D2,L2,V3,M2} { ! before_on_line( X, Y, Z ), alpha2( X, Y, Z )
% 0.42/1.07 }.
% 0.42/1.07 (492) {G0,W11,D2,L3,V3,M3} { ! distinct_points( Y, Z ), ! alpha2( X, Y, Z
% 0.42/1.07 ), before_on_line( X, Y, Z ) }.
% 0.42/1.07 (493) {G0,W7,D2,L2,V3,M2} { ! alpha2( X, Y, Z ), incident_point_and_line(
% 0.42/1.07 Y, X ) }.
% 0.42/1.07 (494) {G0,W8,D2,L2,V3,M2} { ! alpha2( X, Y, Z ), alpha5( X, Y, Z ) }.
% 0.42/1.07 (495) {G0,W11,D2,L3,V3,M3} { ! incident_point_and_line( Y, X ), ! alpha5(
% 0.42/1.07 X, Y, Z ), alpha2( X, Y, Z ) }.
% 0.42/1.07 (496) {G0,W7,D2,L2,V3,M2} { ! alpha5( X, Y, Z ), incident_point_and_line(
% 0.42/1.07 Z, X ) }.
% 0.42/1.07 (497) {G0,W9,D3,L2,V3,M2} { ! alpha5( X, Y, Z ), equally_directed_lines( X
% 0.42/1.07 , line_connecting( Y, Z ) ) }.
% 0.42/1.07 (498) {G0,W12,D3,L3,V3,M3} { ! incident_point_and_line( Z, X ), !
% 0.42/1.07 equally_directed_lines( X, line_connecting( Y, Z ) ), alpha5( X, Y, Z )
% 0.42/1.07 }.
% 0.42/1.07 (499) {G0,W15,D2,L3,V4,M3} { ! between_on_line( X, Y, Z, T ), alpha3( X, Y
% 0.42/1.07 , Z, T ), alpha6( X, Y, Z, T ) }.
% 0.42/1.07 (500) {G0,W10,D2,L2,V4,M2} { ! alpha3( X, Y, Z, T ), between_on_line( X, Y
% 0.42/1.07 , Z, T ) }.
% 0.42/1.07 (501) {G0,W10,D2,L2,V4,M2} { ! alpha6( X, Y, Z, T ), between_on_line( X, Y
% 0.42/1.07 , Z, T ) }.
% 0.42/1.07 (502) {G0,W9,D2,L2,V4,M2} { ! alpha6( X, Y, Z, T ), before_on_line( X, T,
% 0.42/1.07 Z ) }.
% 0.42/1.07 (503) {G0,W9,D2,L2,V4,M2} { ! alpha6( X, Y, Z, T ), before_on_line( X, Z,
% 0.42/1.07 Y ) }.
% 0.42/1.07 (504) {G0,W13,D2,L3,V4,M3} { ! before_on_line( X, T, Z ), ! before_on_line
% 0.42/1.07 ( X, Z, Y ), alpha6( X, Y, Z, T ) }.
% 0.42/1.07 (505) {G0,W9,D2,L2,V4,M2} { ! alpha3( X, Y, Z, T ), before_on_line( X, Y,
% 0.42/1.07 Z ) }.
% 0.42/1.07 (506) {G0,W9,D2,L2,V4,M2} { ! alpha3( X, Y, Z, T ), before_on_line( X, Z,
% 0.42/1.07 T ) }.
% 0.42/1.07 (507) {G0,W13,D2,L3,V4,M3} { ! before_on_line( X, Y, Z ), ! before_on_line
% 0.42/1.07 ( X, Z, T ), alpha3( X, Y, Z, T ) }.
% 0.42/1.07 (508) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 0.42/1.07 (509) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 0.42/1.07 , Z ), distinct_points( Y, Z ) }.
% 0.42/1.07 (510) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.42/1.07 (511) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X, Z
% 0.42/1.07 ), distinct_lines( Y, Z ) }.
% 0.42/1.07 (512) {G0,W3,D2,L1,V1,M1} { equally_directed_lines( X, X ) }.
% 0.42/1.07 (513) {G0,W9,D2,L3,V3,M3} { ! unequally_directed_lines( X, Y ),
% 0.42/1.07 unequally_directed_lines( X, Z ), unequally_directed_lines( Y, Z ) }.
% 0.42/1.07 (514) {G0,W13,D3,L4,V3,M4} { ! unequally_directed_lines( X, Y ), !
% 0.42/1.07 unequally_directed_lines( X, reverse_line( Y ) ), alpha7( X, Z ),
% 0.42/1.07 unequally_directed_lines( Y, Z ) }.
% 0.42/1.07 (515) {G0,W14,D3,L4,V3,M4} { ! unequally_directed_lines( X, Y ), !
% 0.42/1.07 unequally_directed_lines( X, reverse_line( Y ) ), alpha7( X, Z ),
% 0.42/1.07 unequally_directed_lines( Y, reverse_line( Z ) ) }.
% 0.42/1.07 (516) {G0,W6,D2,L2,V2,M2} { ! alpha7( X, Y ), unequally_directed_lines( X
% 0.42/1.07 , Y ) }.
% 0.42/1.07 (517) {G0,W7,D3,L2,V2,M2} { ! alpha7( X, Y ), unequally_directed_lines( X
% 0.42/1.07 , reverse_line( Y ) ) }.
% 0.42/1.07 (518) {G0,W10,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y ), !
% 0.42/1.07 unequally_directed_lines( X, reverse_line( Y ) ), alpha7( X, Y ) }.
% 0.42/1.07 (519) {G0,W7,D3,L2,V2,M2} { unequally_directed_lines( X, Y ),
% 0.42/1.07 unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.42/1.07 (520) {G0,W14,D3,L4,V2,M4} { ! unequally_directed_lines( X, Y ), !
% 0.42/1.07 unequally_directed_lines( X, reverse_line( Y ) ), left_convergent_lines(
% 0.42/1.07 X, Y ), left_convergent_lines( X, reverse_line( Y ) ) }.
% 0.42/1.07 (521) {G0,W3,D2,L1,V2,M1} { ! left_apart_point( X, Y ) }.
% 0.42/1.07 (522) {G0,W4,D3,L1,V2,M1} { ! left_apart_point( X, reverse_line( Y ) ) }.
% 0.42/1.07 (523) {G0,W3,D2,L1,V2,M1} { ! left_convergent_lines( X, Y ) }.
% 0.42/1.07 (524) {G0,W4,D3,L1,V2,M1} { ! left_convergent_lines( X, reverse_line( Y )
% 0.42/1.07 ) }.
% 0.42/1.07 (525) {G0,W11,D3,L4,V2,M4} { ! point( X ), ! point( Y ), ! distinct_points
% 0.42/1.07 ( X, Y ), line( line_connecting( X, Y ) ) }.
% 0.42/1.07 (526) {G0,W15,D3,L5,V2,M5} { ! line( X ), ! line( Y ), !
% 0.42/1.07 unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.42/1.07 reverse_line( Y ) ), point( intersection_point( X, Y ) ) }.
% 0.42/1.07 (527) {G0,W8,D3,L3,V2,M3} { ! point( Y ), ! line( X ), line(
% 0.42/1.07 parallel_through_point( X, Y ) ) }.
% 0.42/1.07 (528) {G0,W5,D3,L2,V1,M2} { ! line( X ), line( reverse_line( X ) ) }.
% 0.42/1.07 (529) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.42/1.07 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 0.42/1.07 (530) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.42/1.07 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 0.42/1.07 (531) {G0,W12,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y ), !
% 0.42/1.07 unequally_directed_lines( X, reverse_line( Y ) ), ! apart_point_and_line
% 0.42/1.07 ( intersection_point( X, Y ), X ) }.
% 0.42/1.07 (532) {G0,W12,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y ), !
% 0.42/1.07 unequally_directed_lines( X, reverse_line( Y ) ), ! apart_point_and_line
% 0.42/1.07 ( intersection_point( X, Y ), Y ) }.
% 0.42/1.07 (533) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.42/1.07 parallel_through_point( Y, X ) ) }.
% 0.42/1.07 (534) {G0,W4,D3,L1,V1,M1} { ! distinct_lines( X, reverse_line( X ) ) }.
% 0.42/1.07 (535) {G0,W11,D4,L2,V2,M2} { ! distinct_points( X, Y ),
% 0.42/1.07 equally_directed_lines( line_connecting( X, Y ), reverse_line(
% 0.42/1.07 line_connecting( Y, X ) ) ) }.
% 0.42/1.07 (536) {G0,W5,D3,L1,V2,M1} { equally_directed_lines( parallel_through_point
% 0.42/1.07 ( Y, X ), Y ) }.
% 0.42/1.07 (537) {G0,W34,D3,L10,V4,M10} { ! distinct_points( X, Y ), ! distinct_lines
% 0.42/1.07 ( Z, T ), left_apart_point( X, Z ), left_apart_point( Y, Z ),
% 0.42/1.07 left_apart_point( X, T ), left_apart_point( Y, T ), left_apart_point( X,
% 0.42/1.07 reverse_line( Z ) ), left_apart_point( Y, reverse_line( Z ) ),
% 0.42/1.07 left_apart_point( X, reverse_line( T ) ), left_apart_point( Y,
% 0.42/1.07 reverse_line( T ) ) }.
% 0.42/1.07 (538) {G0,W14,D3,L4,V3,M4} { ! distinct_points( X, Y ), ! left_apart_point
% 0.42/1.07 ( X, Z ), left_apart_point( Y, Z ), left_convergent_lines(
% 0.42/1.07 line_connecting( X, Y ), Z ) }.
% 0.42/1.07 (539) {G0,W9,D2,L3,V3,M3} { ! left_apart_point( X, Y ), distinct_points( X
% 0.42/1.07 , Z ), left_apart_point( Z, Y ) }.
% 0.42/1.07 (540) {G0,W13,D3,L4,V3,M4} { ! left_apart_point( X, Y ), !
% 0.42/1.07 unequally_directed_lines( Y, Z ), distinct_lines( Y, Z ),
% 0.42/1.07 left_apart_point( X, reverse_line( Z ) ) }.
% 0.42/1.07 (541) {G0,W9,D2,L3,V3,M3} { ! left_convergent_lines( X, Y ),
% 0.42/1.07 unequally_directed_lines( Y, Z ), left_convergent_lines( X, Z ) }.
% 0.42/1.07 (542) {G0,W3,D2,L1,V0,M1} { equally_directed_opposite_lines( skol3, skol1
% 0.42/1.07 ) }.
% 0.42/1.07 (543) {G0,W3,D2,L1,V0,M1} { equally_directed_lines( skol3, skol2 ) }.
% 0.42/1.07 (544) {G0,W3,D2,L1,V0,M1} { ! equally_directed_opposite_lines( skol1,
% 0.42/1.07 skol2 ) }.
% 0.42/1.07
% 0.42/1.07
% 0.42/1.07 Total Proof:
% 0.42/1.07
% 0.42/1.07 subsumption: (0) {G0,W7,D3,L2,V2,M1} I { !
% 0.42/1.07 unequally_directed_opposite_lines( X, Y ), unequally_directed_lines( X,
% 0.42/1.07 reverse_line( Y ) ) }.
% 0.42/1.07 parent0: (465) {G0,W7,D3,L2,V2,M2} { ! unequally_directed_opposite_lines(
% 0.42/1.07 X, Y ), unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.42/1.07 substitution0:
% 0.42/1.07 X := X
% 0.42/1.07 Y := Y
% 0.42/1.07 end
% 0.42/1.07 permutation0:
% 0.42/1.07 0 ==> 0
% 0.42/1.07 1 ==> 1
% 0.42/1.07 end
% 0.42/1.07
% 0.42/1.07 subsumption: (1) {G0,W7,D3,L2,V2,M1} I { unequally_directed_opposite_lines
% 0.42/1.07 ( X, Y ), ! unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.42/1.07 parent0: (466) {G0,W7,D3,L2,V2,M2} { ! unequally_directed_lines( X,
% 0.42/1.07 reverse_line( Y ) ), unequally_directed_opposite_lines( X, Y ) }.
% 0.42/1.07 substitution0:
% 0.42/1.07 X := X
% 0.42/1.07 Y := Y
% 0.42/1.07 end
% 0.42/1.07 permutation0:
% 0.42/1.07 0 ==> 1
% 0.42/1.07 1 ==> 0
% 0.42/1.07 end
% 0.42/1.07
% 0.42/1.07 subsumption: (6) {G0,W6,D2,L2,V2,M1} I { ! unequally_directed_lines( X, Y )
% 0.42/1.07 , ! equally_directed_lines( X, Y ) }.
% 0.42/1.07 parent0: (471) {G0,W6,D2,L2,V2,M2} { ! equally_directed_lines( X, Y ), !
% 0.42/1.07 unequally_directed_lines( X, Y ) }.
% 0.42/1.07 substitution0:
% 0.42/1.07 X := X
% 0.42/1.07 Y := Y
% 0.42/1.07 end
% 0.42/1.07 permutation0:
% 0.42/1.07 0 ==> 1
% 0.42/1.07 1 ==> 0
% 0.42/1.07 end
% 0.42/1.07
% 0.42/1.07 subsumption: (8) {G0,W6,D2,L2,V2,M1} I { !
% 0.42/1.07 unequally_directed_opposite_lines( X, Y ), !
% 0.42/1.07 equally_directed_opposite_lines( X, Y ) }.
% 0.42/1.07 parent0: (473) {G0,W6,D2,L2,V2,M2} { ! equally_directed_opposite_lines( X
% 0.42/1.07 , Y ), ! unequally_directed_opposite_lines( X, Y ) }.
% 0.42/1.07 substitution0:
% 0.42/1.07 X := X
% 0.42/1.07 Y := Y
% 0.42/1.07 end
% 0.42/1.07 permutation0:
% 0.42/1.07 0 ==> 1
% 0.42/1.07 1 ==> 0
% 0.42/1.07 end
% 0.42/1.07
% 0.42/1.07 subsumption: (9) {G0,W6,D2,L2,V2,M1} I { unequally_directed_opposite_lines
% 0.42/1.07 ( X, Y ), equally_directed_opposite_lines( X, Y ) }.
% 0.42/1.07 parent0: (474) {G0,W6,D2,L2,V2,M2} { unequally_directed_opposite_lines( X
% 0.42/1.07 , Y ), equally_directed_opposite_lines( X, Y ) }.
% 0.42/1.07 substitution0:
% 0.42/1.07 X := X
% 0.42/1.07 Y := Y
% 0.42/1.07 end
% 0.42/1.07 permutation0:
% 0.42/1.07 0 ==> 0
% 0.42/1.07 1 ==> 1
% 0.42/1.07 end
% 0.42/1.07
% 0.42/1.07 subsumption: (48) {G0,W9,D2,L3,V3,M3} I { unequally_directed_lines( X, Z )
% 0.42/1.07 , unequally_directed_lines( Y, Z ), ! unequally_directed_lines( X, Y )
% 0.42/1.07 }.
% 0.42/1.07 parent0: (513) {G0,W9,D2,L3,V3,M3} { ! unequally_directed_lines( X, Y ),
% 0.42/1.07 unequally_directed_lines( X, Z ), unequally_directed_lines( Y, Z ) }.
% 0.42/1.07 substitution0:
% 0.42/1.07 X := X
% 0.42/1.07 Y := Y
% 0.42/1.07 Z := Z
% 0.42/1.07 end
% 0.42/1.07 permutation0:
% 0.42/1.07 0 ==> 2
% 0.42/1.07 1 ==> 0
% 0.42/1.07 2 ==> 1
% 0.42/1.07 end
% 0.42/1.07
% 0.42/1.07 subsumption: (54) {G0,W7,D3,L2,V2,M2} I { unequally_directed_lines( X,
% 0.42/1.07 reverse_line( Y ) ), unequally_directed_lines( X, Y ) }.
% 0.42/1.07 parent0: (519) {G0,W7,D3,L2,V2,M2} { unequally_directed_lines( X, Y ),
% 0.42/1.07 unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.42/1.07 substitution0:
% 0.42/1.07 X := X
% 0.42/1.07 Y := Y
% 0.42/1.07 end
% 0.42/1.07 permutation0:
% 0.42/1.07 0 ==> 1
% 0.42/1.07 1 ==> 0
% 0.42/1.07 end
% 0.42/1.07
% 0.42/1.07 subsumption: (55) {G0,W14,D3,L4,V2,M2} I { ! unequally_directed_lines( X, Y
% 0.42/1.07 ), ! unequally_directed_lines( X, reverse_line( Y ) ),
% 0.42/1.07 left_convergent_lines( X, reverse_line( Y ) ), left_convergent_lines( X,
% 0.42/1.07 Y ) }.
% 0.42/1.07 parent0: (520) {G0,W14,D3,L4,V2,M4} { ! unequally_directed_lines( X, Y ),
% 0.42/1.07 ! unequally_directed_lines( X, reverse_line( Y ) ), left_convergent_lines
% 0.42/1.07 ( X, Y ), left_convergent_lines( X, reverse_line( Y ) ) }.
% 0.42/1.07 substitution0:
% 0.42/1.07 X := X
% 0.42/1.07 Y := Y
% 0.42/1.07 end
% 0.42/1.07 permutation0:
% 0.42/1.07 0 ==> 0
% 0.42/1.07 1 ==> 1
% 0.42/1.07 2 ==> 3
% 0.42/1.07 3 ==> 2
% 0.42/1.07 end
% 0.42/1.07
% 0.42/1.07 subsumption: (57) {G0,W3,D2,L1,V2,M1} I { ! left_convergent_lines( X, Y )
% 0.42/1.07 }.
% 0.42/1.07 parent0: (523) {G0,W3,D2,L1,V2,M1} { ! left_convergent_lines( X, Y ) }.
% 0.42/1.07 substitution0:
% 0.42/1.07 X := X
% 0.42/1.07 Y := Y
% 0.42/1.07 end
% 0.42/1.07 permutation0:
% 0.42/1.07 0 ==> 0
% 0.42/1.07 end
% 0.42/1.07
% 0.42/1.07 subsumption: (71) {G0,W3,D2,L1,V0,M1} I { equally_directed_opposite_lines(
% 0.42/1.07 skol3, skol1 ) }.
% 0.42/1.07 parent0: (542) {G0,W3,D2,L1,V0,M1} { equally_directed_opposite_lines(
% 0.42/1.07 skol3, skol1 ) }.
% 0.42/1.07 substitution0:
% 0.42/1.07 end
% 0.42/1.07 permutation0:
% 0.42/1.07 0 ==> 0
% 0.42/1.07 end
% 0.42/1.07
% 0.42/1.07 subsumption: (72) {G0,W3,D2,L1,V0,M1} I { equally_directed_lines( skol3,
% 0.42/1.07 skol2 ) }.
% 0.42/1.07 parent0: (543) {G0,W3,D2,L1,V0,M1} { equally_directed_lines( skol3, skol2
% 0.42/1.07 ) }.
% 0.42/1.07 substitution0:
% 0.42/1.07 end
% 0.42/1.07 permutation0:
% 0.42/1.07 0 ==> 0
% 0.42/1.07 end
% 0.42/1.07
% 0.42/1.07 subsumption: (73) {G0,W3,D2,L1,V0,M1} I { ! equally_directed_opposite_lines
% 0.42/1.07 ( skol1, skol2 ) }.
% 0.42/1.07 parent0: (544) {G0,W3,D2,L1,V0,M1} { ! equally_directed_opposite_lines(
% 0.42/1.07 skol1, skol2 ) }.
% 0.42/1.07 substitution0:
% 0.42/1.07 end
% 0.42/1.07 permutation0:
% 0.42/1.07 0 ==> 0
% 0.42/1.07 end
% 0.42/1.07
% 0.42/1.07 resolution: (664) {G1,W3,D2,L1,V0,M1} { unequally_directed_opposite_lines
% 0.42/1.07 ( skol1, skol2 ) }.
% 0.42/1.07 parent0[0]: (73) {G0,W3,D2,L1,V0,M1} I { ! equally_directed_opposite_lines
% 0.42/1.07 ( skol1, skol2 ) }.
% 0.42/1.07 parent1[1]: (9) {G0,W6,D2,L2,V2,M1} I { unequally_directed_opposite_lines(
% 0.42/1.07 X, Y ), equally_directed_opposite_lines( X, Y ) }.
% 0.42/1.07 substitution0:
% 0.42/1.07 end
% 0.42/1.07 substitution1:
% 0.42/1.07 X := skol1
% 0.42/1.07 Y := skol2
% 0.42/1.07 end
% 0.42/1.07
% 0.42/1.07 subsumption: (83) {G1,W3,D2,L1,V0,M1} R(9,73) {
% 0.42/1.07 unequally_directed_opposite_lines( skol1, skol2 ) }.
% 0.42/1.07 parent0: (664) {G1,W3,D2,L1,V0,M1} { unequally_directed_opposite_lines(
% 0.42/1.07 skol1, skol2 ) }.
% 0.42/1.07 substitution0:
% 0.42/1.07 end
% 0.42/1.07 permutation0:
% 0.42/1.07 0 ==> 0
% 0.42/1.07 end
% 0.42/1.07
% 0.42/1.07 resolution: (665) {G1,W3,D2,L1,V0,M1} { !
% 0.42/1.07 unequally_directed_opposite_lines( skol3, skol1 ) }.
% 0.42/1.07 parent0[1]: (8) {G0,W6,D2,L2,V2,M1} I { ! unequally_directed_opposite_lines
% 0.42/1.07 ( X, Y ), ! equally_directed_opposite_lines( X, Y ) }.
% 0.42/1.07 parent1[0]: (71) {G0,W3,D2,L1,V0,M1} I { equally_directed_opposite_lines(
% 0.42/1.07 skol3, skol1 ) }.
% 0.42/1.07 substitution0:
% 0.42/1.07 X := skol3
% 0.42/1.07 Y := skol1
% 0.42/1.07 end
% 0.42/1.07 substitution1:
% 0.42/1.07 end
% 0.42/1.07
% 0.42/1.07 subsumption: (85) {G1,W3,D2,L1,V0,M1} R(8,71) { !
% 0.42/1.07 unequally_directed_opposite_lines( skol3, skol1 ) }.
% 0.42/1.07 parent0: (665) {G1,W3,D2,L1,V0,M1} { ! unequally_directed_opposite_lines(
% 0.42/1.07 skol3, skol1 ) }.
% 0.42/1.07 substitution0:
% 0.42/1.07 end
% 0.42/1.07 permutation0:
% 0.42/1.07 0 ==> 0
% 0.42/1.07 end
% 0.42/1.07
% 0.42/1.07 resolution: (666) {G1,W3,D2,L1,V0,M1} { ! unequally_directed_lines( skol3
% 0.42/1.07 , skol2 ) }.
% 0.42/1.07 parent0[1]: (6) {G0,W6,D2,L2,V2,M1} I { ! unequally_directed_lines( X, Y )
% 0.42/1.07 , ! equally_directed_lines( X, Y ) }.
% 0.42/1.07 parent1[0]: (72) {G0,W3,D2,L1,V0,M1} I { equally_directed_lines( skol3,
% 0.42/1.07 skol2 ) }.
% 0.42/1.07 substitution0:
% 0.42/1.07 X := skol3
% 0.42/1.07 Y := skol2
% 0.42/1.07 end
% 0.42/1.07 substitution1:
% 0.42/1.07 end
% 0.42/1.07
% 0.42/1.07 subsumption: (87) {G1,W3,D2,L1,V0,M1} R(6,72) { ! unequally_directed_lines
% 0.42/1.07 ( skol3, skol2 ) }.
% 0.42/1.07 parent0: (666) {G1,W3,D2,L1,V0,M1} { ! unequally_directed_lines( skol3,
% 0.42/1.07 skol2 ) }.
% 0.42/1.07 substitution0:
% 0.42/1.07 end
% 0.42/1.07 permutation0:
% 0.42/1.07 0 ==> 0
% 0.42/1.07 end
% 0.42/1.07
% 0.42/1.07 resolution: (667) {G1,W6,D2,L2,V2,M2} { unequally_directed_opposite_lines
% 0.42/1.07 ( X, Y ), unequally_directed_lines( X, Y ) }.
% 0.42/1.07 parent0[1]: (1) {G0,W7,D3,L2,V2,M1} I { unequally_directed_opposite_lines(
% 0.42/1.07 X, Y ), ! unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.42/1.07 parent1[0]: (54) {G0,W7,D3,L2,V2,M2} I { unequally_directed_lines( X,
% 0.42/1.07 reverse_line( Y ) ), unequally_directed_lines( X, Y ) }.
% 0.42/1.07 substitution0:
% 0.42/1.07 X := X
% 0.42/1.07 Y := Y
% 0.42/1.07 end
% 0.42/1.07 substitution1:
% 0.42/1.07 X := X
% 0.42/1.07 Y := Y
% 0.42/1.07 end
% 0.42/1.07
% 0.42/1.07 subsumption: (102) {G1,W6,D2,L2,V2,M1} R(54,1) {
% 0.42/1.07 unequally_directed_opposite_lines( X, Y ), unequally_directed_lines( X, Y
% 0.42/1.07 ) }.
% 0.42/1.07 parent0: (667) {G1,W6,D2,L2,V2,M2} { unequally_directed_opposite_lines( X
% 0.42/1.07 , Y ), unequally_directed_lines( X, Y ) }.
% 0.42/1.07 substitution0:
% 0.42/1.07 X := X
% 0.42/1.07 Y := Y
% 0.42/1.07 end
% 0.42/1.07 permutation0:
% 0.42/1.07 0 ==> 0
% 0.42/1.07 1 ==> 1
% 0.42/1.07 end
% 0.42/1.07
% 0.42/1.07 resolution: (669) {G1,W6,D2,L2,V1,M2} { unequally_directed_lines( X, skol2
% 0.42/1.07 ), ! unequally_directed_lines( skol3, X ) }.
% 0.42/1.07 parent0[0]: (87) {G1,W3,D2,L1,V0,M1} R(6,72) { ! unequally_directed_lines(
% 0.42/1.07 skol3, skol2 ) }.
% 0.42/1.07 parent1[0]: (48) {G0,W9,D2,L3,V3,M3} I { unequally_directed_lines( X, Z ),
% 0.42/1.07 unequally_directed_lines( Y, Z ), ! unequally_directed_lines( X, Y ) }.
% 0.42/1.07 substitution0:
% 0.42/1.07 end
% 0.42/1.07 substitution1:
% 0.42/1.07 X := skol3
% 0.42/1.07 Y := X
% 0.42/1.07 Z := skol2
% 0.42/1.07 end
% 0.42/1.07
% 0.42/1.07 subsumption: (141) {G2,W6,D2,L2,V1,M2} R(48,87) { !
% 0.42/1.07 unequally_directed_lines( skol3, X ), unequally_directed_lines( X, skol2
% 0.42/1.07 ) }.
% 0.42/1.07 parent0: (669) {G1,W6,D2,L2,V1,M2} { unequally_directed_lines( X, skol2 )
% 0.42/1.07 , ! unequally_directed_lines( skol3, X ) }.
% 0.42/1.07 substitution0:
% 0.42/1.07 X := X
% 0.42/1.07 end
% 0.42/1.07 permutation0:
% 0.42/1.07 0 ==> 1
% 0.42/1.07 1 ==> 0
% 0.42/1.07 end
% 0.42/1.07
% 0.42/1.07 resolution: (671) {G2,W6,D2,L2,V1,M2} { unequally_directed_lines( X, skol2
% 0.42/1.07 ), unequally_directed_opposite_lines( skol3, X ) }.
% 0.42/1.07 parent0[0]: (141) {G2,W6,D2,L2,V1,M2} R(48,87) { ! unequally_directed_lines
% 0.42/1.07 ( skol3, X ), unequally_directed_lines( X, skol2 ) }.
% 0.42/1.07 parent1[1]: (102) {G1,W6,D2,L2,V2,M1} R(54,1) {
% 0.42/1.07 unequally_directed_opposite_lines( X, Y ), unequally_directed_lines( X, Y
% 0.42/1.07 ) }.
% 0.42/1.07 substitution0:
% 0.42/1.07 X := X
% 0.42/1.07 end
% 0.42/1.07 substitution1:
% 0.42/1.07 X := skol3
% 0.42/1.07 Y := X
% 0.42/1.07 end
% 0.42/1.07
% 0.42/1.07 subsumption: (216) {G3,W6,D2,L2,V1,M1} R(141,102) {
% 0.42/1.07 unequally_directed_opposite_lines( skol3, X ), unequally_directed_lines(
% 0.42/1.07 X, skol2 ) }.
% 0.42/1.07 parent0: (671) {G2,W6,D2,L2,V1,M2} { unequally_directed_lines( X, skol2 )
% 0.42/1.07 , unequally_directed_opposite_lines( skol3, X ) }.
% 0.42/1.07 substitution0:
% 0.42/1.07 X := X
% 0.42/1.07 end
% 0.42/1.07 permutation0:
% 0.42/1.07 0 ==> 1
% 0.42/1.07 1 ==> 0
% 0.42/1.07 end
% 0.42/1.07
% 0.42/1.07 resolution: (672) {G1,W10,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y
% 0.42/1.07 ), ! unequally_directed_lines( X, reverse_line( Y ) ),
% 0.42/1.07 left_convergent_lines( X, Y ) }.
% 0.42/1.07 parent0[0]: (57) {G0,W3,D2,L1,V2,M1} I { ! left_convergent_lines( X, Y )
% 0.42/1.07 }.
% 0.42/1.07 parent1[2]: (55) {G0,W14,D3,L4,V2,M2} I { ! unequally_directed_lines( X, Y
% 0.42/1.07 ), ! unequally_directed_lines( X, reverse_line( Y ) ),
% 0.42/1.07 left_convergent_lines( X, reverse_line( Y ) ), left_convergent_lines( X,
% 0.42/1.07 Y ) }.
% 0.42/1.07 substitution0:
% 0.42/1.07 X := X
% 0.42/1.07 Y := reverse_line( Y )
% 0.42/1.07 end
% 0.42/1.07 substitution1:
% 0.42/1.07 X := X
% 0.42/1.07 Y := Y
% 0.42/1.07 end
% 0.42/1.07
% 0.42/1.07 resolution: (674) {G1,W7,D3,L2,V2,M2} { ! unequally_directed_lines( X, Y )
% 0.42/1.07 , ! unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.42/1.07 parent0[0]: (57) {G0,W3,D2,L1,V2,M1} I { ! left_convergent_lines( X, Y )
% 0.42/1.07 }.
% 0.42/1.07 parent1[2]: (672) {G1,W10,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y
% 0.42/1.07 ), ! unequally_directed_lines( X, reverse_line( Y ) ),
% 0.42/1.07 left_convergent_lines( X, Y ) }.
% 0.42/1.07 substitution0:
% 0.42/1.07 X := X
% 0.42/1.07 Y := Y
% 0.42/1.07 end
% 0.42/1.07 substitution1:
% 0.42/1.07 X := X
% 0.42/1.07 Y := Y
% 0.42/1.07 end
% 0.42/1.07
% 0.42/1.07 subsumption: (267) {G1,W7,D3,L2,V2,M2} S(55);r(57);r(57) { !
% 0.42/1.07 unequally_directed_lines( X, reverse_line( Y ) ), !
% 0.42/1.07 unequally_directed_lines( X, Y ) }.
% 0.42/1.07 parent0: (674) {G1,W7,D3,L2,V2,M2} { ! unequally_directed_lines( X, Y ), !
% 0.42/1.07 unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.42/1.07 substitution0:
% 0.42/1.07 X := X
% 0.42/1.07 Y := Y
% 0.42/1.07 end
% 0.42/1.07 permutation0:
% 0.42/1.07 0 ==> 1
% 0.42/1.07 1 ==> 0
% 0.42/1.07 end
% 0.42/1.07
% 0.42/1.07 resolution: (675) {G1,W6,D2,L2,V2,M2} { ! unequally_directed_lines( X, Y )
% 0.42/1.07 , ! unequally_directed_opposite_lines( X, Y ) }.
% 0.42/1.07 parent0[0]: (267) {G1,W7,D3,L2,V2,M2} S(55);r(57);r(57) { !
% 0.42/1.07 unequally_directed_lines( X, reverse_line( Y ) ), !
% 0.42/1.07 unequally_directed_lines( X, Y ) }.
% 0.42/1.07 parent1[1]: (0) {G0,W7,D3,L2,V2,M1} I { ! unequally_directed_opposite_lines
% 0.42/1.07 ( X, Y ), unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.42/1.07 substitution0:
% 0.42/1.07 X := X
% 0.42/1.07 Y := Y
% 0.42/1.07 end
% 0.42/1.07 substitution1:
% 0.42/1.07 X := X
% 0.42/1.07 Y := Y
% 0.42/1.07 end
% 0.42/1.07
% 0.42/1.07 subsumption: (338) {G2,W6,D2,L2,V2,M1} R(267,0) { !
% 0.42/1.07 unequally_directed_opposite_lines( X, Y ), ! unequally_directed_lines( X
% 0.42/1.07 , Y ) }.
% 0.42/1.07 parent0: (675) {G1,W6,D2,L2,V2,M2} { ! unequally_directed_lines( X, Y ), !
% 0.42/1.07 unequally_directed_opposite_lines( X, Y ) }.
% 0.42/1.07 substitution0:
% 0.42/1.07 X := X
% 0.42/1.07 Y := Y
% 0.42/1.07 end
% 0.42/1.07 permutation0:
% 0.42/1.07 0 ==> 1
% 0.42/1.07 1 ==> 0
% 0.42/1.07 end
% 0.42/1.07
% 0.42/1.07 resolution: (678) {G3,W6,D2,L2,V1,M2} { !
% 0.42/1.07 unequally_directed_opposite_lines( X, skol2 ),
% 0.42/1.07 unequally_directed_opposite_lines( skol3, X ) }.
% 0.42/1.07 parent0[1]: (338) {G2,W6,D2,L2,V2,M1} R(267,0) { !
% 0.42/1.07 unequally_directed_opposite_lines( X, Y ), ! unequally_directed_lines( X
% 0.42/1.07 , Y ) }.
% 0.42/1.07 parent1[1]: (216) {G3,W6,D2,L2,V1,M1} R(141,102) {
% 0.42/1.07 unequally_directed_opposite_lines( skol3, X ), unequally_directed_lines(
% 0.42/1.07 X, skol2 ) }.
% 0.42/1.07 substitution0:
% 0.42/1.07 X := X
% 0.42/1.07 Y := skol2
% 0.42/1.07 end
% 0.42/1.07 substitution1:
% 0.42/1.07 X := X
% 0.42/1.07 end
% 0.42/1.07
% 0.42/1.07 subsumption: (400) {G4,W6,D2,L2,V1,M2} R(338,216) {
% 0.42/1.07 unequally_directed_opposite_lines( skol3, X ), !
% 0.42/1.07 unequally_directed_opposite_lines( X, skol2 ) }.
% 0.42/1.07 parent0: (678) {G3,W6,D2,L2,V1,M2} { ! unequally_directed_opposite_lines(
% 0.42/1.07 X, skol2 ), unequally_directed_opposite_lines( skol3, X ) }.
% 0.42/1.07 substitution0:
% 0.42/1.07 X := X
% 0.42/1.07 end
% 0.42/1.07 permutation0:
% 0.42/1.07 0 ==> 1
% 0.42/1.07 1 ==> 0
% 0.42/1.07 end
% 0.42/1.07
% 0.42/1.07 resolution: (679) {G2,W3,D2,L1,V0,M1} { !
% 0.42/1.07 unequally_directed_opposite_lines( skol1, skol2 ) }.
% 0.42/1.07 parent0[0]: (85) {G1,W3,D2,L1,V0,M1} R(8,71) { !
% 0.42/1.07 unequally_directed_opposite_lines( skol3, skol1 ) }.
% 0.42/1.07 parent1[0]: (400) {G4,W6,D2,L2,V1,M2} R(338,216) {
% 0.42/1.07 unequally_directed_opposite_lines( skol3, X ), !
% 0.42/1.07 unequally_directed_opposite_lines( X, skol2 ) }.
% 0.42/1.07 substitution0:
% 0.42/1.07 end
% 0.42/1.07 substitution1:
% 0.42/1.07 X := skol1
% 0.42/1.07 end
% 0.42/1.07
% 0.42/1.07 resolution: (680) {G2,W0,D0,L0,V0,M0} { }.
% 0.42/1.07 parent0[0]: (679) {G2,W3,D2,L1,V0,M1} { !
% 0.42/1.07 unequally_directed_opposite_lines( skol1, skol2 ) }.
% 0.42/1.07 parent1[0]: (83) {G1,W3,D2,L1,V0,M1} R(9,73) {
% 0.42/1.07 unequally_directed_opposite_lines( skol1, skol2 ) }.
% 0.42/1.07 substitution0:
% 0.42/1.07 end
% 0.42/1.07 substitution1:
% 0.42/1.07 end
% 0.42/1.07
% 0.42/1.07 subsumption: (463) {G5,W0,D0,L0,V0,M0} R(400,85);r(83) { }.
% 0.42/1.07 parent0: (680) {G2,W0,D0,L0,V0,M0} { }.
% 0.42/1.07 substitution0:
% 0.42/1.07 end
% 0.42/1.07 permutation0:
% 0.42/1.07 end
% 0.42/1.07
% 0.42/1.07 Proof check complete!
% 0.42/1.07
% 0.42/1.07 Memory use:
% 0.42/1.07
% 0.42/1.07 space for terms: 5782
% 0.42/1.07 space for clauses: 24142
% 0.42/1.07
% 0.42/1.07
% 0.42/1.07 clauses generated: 1163
% 0.42/1.07 clauses kept: 464
% 0.42/1.07 clauses selected: 175
% 0.42/1.07 clauses deleted: 25
% 0.42/1.07 clauses inuse deleted: 0
% 0.42/1.07
% 0.42/1.07 subsentry: 3688
% 0.42/1.07 literals s-matched: 2302
% 0.42/1.07 literals matched: 2152
% 0.42/1.07 full subsumption: 526
% 0.42/1.07
% 0.42/1.07 checksum: 1099386242
% 0.42/1.07
% 0.42/1.07
% 0.42/1.07 Bliksem ended
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