TSTP Solution File: GEO232+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO232+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n024.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 0.71s 1.10s
% Output : Refutation 0.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO232+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.07/0.13 % Command : bliksem %s
% 0.14/0.34 % Computer : n024.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % DateTime : Sat Jun 18 12:55:02 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.71/1.10 *** allocated 10000 integers for termspace/termends
% 0.71/1.10 *** allocated 10000 integers for clauses
% 0.71/1.10 *** allocated 10000 integers for justifications
% 0.71/1.10 Bliksem 1.12
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 Automatic Strategy Selection
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 Clauses:
% 0.71/1.10
% 0.71/1.10 { ! apart_point_and_line( X, Y ), left_apart_point( X, Y ),
% 0.71/1.10 left_apart_point( X, reverse_line( Y ) ) }.
% 0.71/1.10 { ! left_apart_point( X, Y ), apart_point_and_line( X, Y ) }.
% 0.71/1.10 { ! left_apart_point( X, reverse_line( Y ) ), apart_point_and_line( X, Y )
% 0.71/1.10 }.
% 0.71/1.10 { ! convergent_lines( X, Y ), unequally_directed_lines( X, Y ) }.
% 0.71/1.10 { ! convergent_lines( X, Y ), unequally_directed_lines( X, reverse_line( Y
% 0.71/1.10 ) ) }.
% 0.71/1.10 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.71/1.10 reverse_line( Y ) ), convergent_lines( X, Y ) }.
% 0.71/1.10 { ! divides_points( Z, X, Y ), alpha1( X, Y, Z ), alpha4( X, Y, Z ) }.
% 0.71/1.10 { ! alpha1( X, Y, Z ), divides_points( Z, X, Y ) }.
% 0.71/1.10 { ! alpha4( X, Y, Z ), divides_points( Z, X, Y ) }.
% 0.71/1.10 { ! alpha4( X, Y, Z ), left_apart_point( X, reverse_line( Z ) ) }.
% 0.71/1.10 { ! alpha4( X, Y, Z ), left_apart_point( Y, Z ) }.
% 0.71/1.10 { ! left_apart_point( X, reverse_line( Z ) ), ! left_apart_point( Y, Z ),
% 0.71/1.10 alpha4( X, Y, Z ) }.
% 0.71/1.10 { ! alpha1( X, Y, Z ), left_apart_point( X, Z ) }.
% 0.71/1.10 { ! alpha1( X, Y, Z ), left_apart_point( Y, reverse_line( Z ) ) }.
% 0.71/1.10 { ! left_apart_point( X, Z ), ! left_apart_point( Y, reverse_line( Z ) ),
% 0.71/1.10 alpha1( X, Y, Z ) }.
% 0.71/1.10 { ! before_on_line( X, Y, Z ), distinct_points( Y, Z ) }.
% 0.71/1.10 { ! before_on_line( X, Y, Z ), alpha7( X, Y, Z ) }.
% 0.71/1.10 { ! distinct_points( Y, Z ), ! alpha7( X, Y, Z ), before_on_line( X, Y, Z )
% 0.71/1.10 }.
% 0.71/1.10 { ! alpha7( X, Y, Z ), alpha2( X, Y ) }.
% 0.71/1.10 { ! alpha7( X, Y, Z ), alpha8( X, Y, Z ) }.
% 0.71/1.10 { ! alpha2( X, Y ), ! alpha8( X, Y, Z ), alpha7( X, Y, Z ) }.
% 0.71/1.10 { ! alpha8( X, Y, Z ), alpha5( X, Z ) }.
% 0.71/1.10 { ! alpha8( X, Y, Z ), ! unequally_directed_lines( X, line_connecting( Y, Z
% 0.71/1.10 ) ) }.
% 0.71/1.10 { ! alpha5( X, Z ), unequally_directed_lines( X, line_connecting( Y, Z ) )
% 0.71/1.10 , alpha8( X, Y, Z ) }.
% 0.71/1.10 { ! alpha5( X, Y ), ! left_apart_point( Y, X ) }.
% 0.71/1.10 { ! alpha5( X, Y ), ! left_apart_point( Y, reverse_line( X ) ) }.
% 0.71/1.10 { left_apart_point( Y, X ), left_apart_point( Y, reverse_line( X ) ),
% 0.71/1.10 alpha5( X, Y ) }.
% 0.71/1.10 { ! alpha2( X, Y ), ! left_apart_point( Y, X ) }.
% 0.71/1.10 { ! alpha2( X, Y ), ! left_apart_point( Y, reverse_line( X ) ) }.
% 0.71/1.10 { left_apart_point( Y, X ), left_apart_point( Y, reverse_line( X ) ),
% 0.71/1.10 alpha2( X, Y ) }.
% 0.71/1.10 { ! between_on_line( X, Y, Z, T ), alpha3( X, Y, Z, T ), alpha6( X, Y, Z, T
% 0.71/1.10 ) }.
% 0.71/1.10 { ! alpha3( X, Y, Z, T ), between_on_line( X, Y, Z, T ) }.
% 0.71/1.10 { ! alpha6( X, Y, Z, T ), between_on_line( X, Y, Z, T ) }.
% 0.71/1.10 { ! alpha6( X, Y, Z, T ), before_on_line( X, T, Z ) }.
% 0.71/1.10 { ! alpha6( X, Y, Z, T ), before_on_line( X, Z, Y ) }.
% 0.71/1.10 { ! before_on_line( X, T, Z ), ! before_on_line( X, Z, Y ), alpha6( X, Y, Z
% 0.71/1.10 , T ) }.
% 0.71/1.10 { ! alpha3( X, Y, Z, T ), before_on_line( X, Y, Z ) }.
% 0.71/1.10 { ! alpha3( X, Y, Z, T ), before_on_line( X, Z, T ) }.
% 0.71/1.10 { ! before_on_line( X, Y, Z ), ! before_on_line( X, Z, T ), alpha3( X, Y, Z
% 0.71/1.10 , T ) }.
% 0.71/1.10 { ! distinct_points( X, X ) }.
% 0.71/1.10 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 0.71/1.10 ) }.
% 0.71/1.10 { ! distinct_lines( X, X ) }.
% 0.71/1.10 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.71/1.10 }.
% 0.71/1.10 { ! unequally_directed_lines( X, X ) }.
% 0.71/1.10 { ! unequally_directed_lines( X, Y ), unequally_directed_lines( X, Z ),
% 0.71/1.10 unequally_directed_lines( Y, Z ) }.
% 0.71/1.10 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.71/1.10 reverse_line( Y ) ), alpha9( X, Z ), unequally_directed_lines( Y, Z ) }.
% 0.71/1.10 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.71/1.10 reverse_line( Y ) ), alpha9( X, Z ), unequally_directed_lines( Y,
% 0.71/1.10 reverse_line( Z ) ) }.
% 0.71/1.10 { ! alpha9( X, Y ), unequally_directed_lines( X, Y ) }.
% 0.71/1.10 { ! alpha9( X, Y ), unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.71/1.10 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.71/1.10 reverse_line( Y ) ), alpha9( X, Y ) }.
% 0.71/1.10 { ! line( X ), ! line( Y ), unequally_directed_lines( X, Y ),
% 0.71/1.10 unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.71/1.10 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.71/1.10 reverse_line( Y ) ), left_convergent_lines( X, Y ), left_convergent_lines
% 0.71/1.10 ( X, reverse_line( Y ) ) }.
% 0.71/1.10 { ! left_apart_point( X, Y ) }.
% 0.71/1.10 { ! left_apart_point( X, reverse_line( Y ) ) }.
% 0.71/1.10 { ! left_convergent_lines( X, Y ) }.
% 0.71/1.10 { ! left_convergent_lines( X, reverse_line( Y ) ) }.
% 0.71/1.10 { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line(
% 0.71/1.10 line_connecting( X, Y ) ) }.
% 0.71/1.10 { ! line( X ), ! line( Y ), ! unequally_directed_lines( X, Y ), !
% 0.71/1.10 unequally_directed_lines( X, reverse_line( Y ) ), point(
% 0.71/1.10 intersection_point( X, Y ) ) }.
% 0.71/1.10 { ! point( Y ), ! line( X ), line( parallel_through_point( X, Y ) ) }.
% 0.71/1.10 { ! line( X ), line( reverse_line( X ) ) }.
% 0.71/1.10 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 0.71/1.10 , Y ) ) }.
% 0.71/1.10 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 0.71/1.10 , Y ) ) }.
% 0.71/1.10 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.71/1.10 reverse_line( Y ) ), ! apart_point_and_line( intersection_point( X, Y ),
% 0.71/1.10 X ) }.
% 0.71/1.10 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.71/1.10 reverse_line( Y ) ), ! apart_point_and_line( intersection_point( X, Y ),
% 0.71/1.10 Y ) }.
% 0.71/1.10 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 0.71/1.10 { ! distinct_lines( X, reverse_line( X ) ) }.
% 0.71/1.10 { ! unequally_directed_lines( line_connecting( X, Y ), reverse_line(
% 0.71/1.10 line_connecting( Y, X ) ) ) }.
% 0.71/1.10 { ! unequally_directed_lines( parallel_through_point( Y, X ), Y ) }.
% 0.71/1.10 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), left_apart_point( X
% 0.71/1.10 , Z ), left_apart_point( Y, Z ), left_apart_point( X, T ),
% 0.71/1.10 left_apart_point( Y, T ), left_apart_point( X, reverse_line( Z ) ),
% 0.71/1.10 left_apart_point( Y, reverse_line( Z ) ), left_apart_point( X,
% 0.71/1.10 reverse_line( T ) ), left_apart_point( Y, reverse_line( T ) ) }.
% 0.71/1.10 { ! distinct_points( X, Y ), ! left_apart_point( X, Z ), left_apart_point(
% 0.71/1.10 Y, Z ), left_convergent_lines( line_connecting( X, Y ), Z ) }.
% 0.71/1.10 { ! left_apart_point( X, Y ), distinct_points( X, Z ), left_apart_point( Z
% 0.71/1.10 , Y ) }.
% 0.71/1.10 { ! left_apart_point( X, Y ), ! unequally_directed_lines( Y, Z ),
% 0.71/1.10 distinct_lines( Y, Z ), left_apart_point( X, reverse_line( Z ) ) }.
% 0.71/1.10 { ! left_convergent_lines( X, Y ), unequally_directed_lines( Y, Z ),
% 0.71/1.10 left_convergent_lines( X, Z ) }.
% 0.71/1.10 { line( skol1 ) }.
% 0.71/1.10 { ! unequally_directed_lines( skol1, reverse_line( skol1 ) ) }.
% 0.71/1.10
% 0.71/1.10 percentage equality = 0.000000, percentage horn = 0.797101
% 0.71/1.10 This a non-horn, non-equality problem
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 Options Used:
% 0.71/1.10
% 0.71/1.10 useres = 1
% 0.71/1.10 useparamod = 0
% 0.71/1.10 useeqrefl = 0
% 0.71/1.10 useeqfact = 0
% 0.71/1.10 usefactor = 1
% 0.71/1.10 usesimpsplitting = 0
% 0.71/1.10 usesimpdemod = 0
% 0.71/1.10 usesimpres = 3
% 0.71/1.10
% 0.71/1.10 resimpinuse = 1000
% 0.71/1.10 resimpclauses = 20000
% 0.71/1.10 substype = standard
% 0.71/1.10 backwardsubs = 1
% 0.71/1.10 selectoldest = 5
% 0.71/1.10
% 0.71/1.10 litorderings [0] = split
% 0.71/1.10 litorderings [1] = liftord
% 0.71/1.10
% 0.71/1.10 termordering = none
% 0.71/1.10
% 0.71/1.10 litapriori = 1
% 0.71/1.10 termapriori = 0
% 0.71/1.10 litaposteriori = 0
% 0.71/1.10 termaposteriori = 0
% 0.71/1.10 demodaposteriori = 0
% 0.71/1.10 ordereqreflfact = 0
% 0.71/1.10
% 0.71/1.10 litselect = none
% 0.71/1.10
% 0.71/1.10 maxweight = 15
% 0.71/1.10 maxdepth = 30000
% 0.71/1.10 maxlength = 115
% 0.71/1.10 maxnrvars = 195
% 0.71/1.10 excuselevel = 1
% 0.71/1.10 increasemaxweight = 1
% 0.71/1.10
% 0.71/1.10 maxselected = 10000000
% 0.71/1.10 maxnrclauses = 10000000
% 0.71/1.10
% 0.71/1.10 showgenerated = 0
% 0.71/1.10 showkept = 0
% 0.71/1.10 showselected = 0
% 0.71/1.10 showdeleted = 0
% 0.71/1.10 showresimp = 1
% 0.71/1.10 showstatus = 2000
% 0.71/1.10
% 0.71/1.10 prologoutput = 0
% 0.71/1.10 nrgoals = 5000000
% 0.71/1.10 totalproof = 1
% 0.71/1.10
% 0.71/1.10 Symbols occurring in the translation:
% 0.71/1.10
% 0.71/1.10 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.71/1.10 . [1, 2] (w:1, o:21, a:1, s:1, b:0),
% 0.71/1.10 ! [4, 1] (w:0, o:13, a:1, s:1, b:0),
% 0.71/1.10 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.71/1.10 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.71/1.10 apart_point_and_line [37, 2] (w:1, o:45, a:1, s:1, b:0),
% 0.71/1.10 left_apart_point [38, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.71/1.10 reverse_line [39, 1] (w:1, o:18, a:1, s:1, b:0),
% 0.71/1.10 convergent_lines [41, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.71/1.10 unequally_directed_lines [42, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.71/1.10 divides_points [44, 3] (w:1, o:58, a:1, s:1, b:0),
% 0.71/1.10 before_on_line [45, 3] (w:1, o:63, a:1, s:1, b:0),
% 0.71/1.10 distinct_points [46, 2] (w:1, o:49, a:1, s:1, b:0),
% 0.71/1.10 line_connecting [47, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.71/1.10 between_on_line [49, 4] (w:1, o:66, a:1, s:1, b:0),
% 0.71/1.10 distinct_lines [50, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.71/1.10 line [52, 1] (w:1, o:19, a:1, s:1, b:0),
% 0.71/1.10 left_convergent_lines [53, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.71/1.10 point [54, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.71/1.10 intersection_point [55, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.71/1.10 parallel_through_point [56, 2] (w:1, o:54, a:1, s:1, b:0),
% 0.71/1.10 alpha1 [57, 3] (w:1, o:59, a:1, s:1, b:0),
% 0.71/1.10 alpha2 [58, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.71/1.10 alpha3 [59, 4] (w:1, o:64, a:1, s:1, b:0),
% 0.71/1.10 alpha4 [60, 3] (w:1, o:60, a:1, s:1, b:0),
% 0.71/1.10 alpha5 [61, 2] (w:1, o:56, a:1, s:1, b:0),
% 0.71/1.10 alpha6 [62, 4] (w:1, o:65, a:1, s:1, b:0),
% 0.71/1.10 alpha7 [63, 3] (w:1, o:61, a:1, s:1, b:0),
% 0.71/1.10 alpha8 [64, 3] (w:1, o:62, a:1, s:1, b:0),
% 0.71/1.10 alpha9 [65, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.71/1.10 skol1 [66, 0] (w:1, o:12, a:1, s:1, b:0).
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 Starting Search:
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 Bliksems!, er is een bewijs:
% 0.71/1.10 % SZS status Theorem
% 0.71/1.10 % SZS output start Refutation
% 0.71/1.10
% 0.71/1.10 (43) {G0,W3,D2,L1,V1,M1} I { ! unequally_directed_lines( X, X ) }.
% 0.71/1.10 (50) {G0,W11,D3,L4,V2,M2} I { ! line( X ), ! line( Y ),
% 0.71/1.10 unequally_directed_lines( X, reverse_line( Y ) ),
% 0.71/1.10 unequally_directed_lines( X, Y ) }.
% 0.71/1.10 (67) {G0,W2,D2,L1,V0,M1} I { line( skol1 ) }.
% 0.71/1.10 (68) {G0,W4,D3,L1,V0,M1} I { ! unequally_directed_lines( skol1,
% 0.71/1.10 reverse_line( skol1 ) ) }.
% 0.71/1.10 (71) {G1,W6,D3,L2,V1,M1} F(50);r(43) { ! line( X ),
% 0.71/1.10 unequally_directed_lines( X, reverse_line( X ) ) }.
% 0.71/1.10 (83) {G2,W0,D0,L0,V0,M0} R(71,68);r(67) { }.
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 % SZS output end Refutation
% 0.71/1.10 found a proof!
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 Unprocessed initial clauses:
% 0.71/1.10
% 0.71/1.10 (85) {G0,W10,D3,L3,V2,M3} { ! apart_point_and_line( X, Y ),
% 0.71/1.10 left_apart_point( X, Y ), left_apart_point( X, reverse_line( Y ) ) }.
% 0.71/1.10 (86) {G0,W6,D2,L2,V2,M2} { ! left_apart_point( X, Y ),
% 0.71/1.10 apart_point_and_line( X, Y ) }.
% 0.71/1.10 (87) {G0,W7,D3,L2,V2,M2} { ! left_apart_point( X, reverse_line( Y ) ),
% 0.71/1.10 apart_point_and_line( X, Y ) }.
% 0.71/1.10 (88) {G0,W6,D2,L2,V2,M2} { ! convergent_lines( X, Y ),
% 0.71/1.10 unequally_directed_lines( X, Y ) }.
% 0.71/1.10 (89) {G0,W7,D3,L2,V2,M2} { ! convergent_lines( X, Y ),
% 0.71/1.10 unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.71/1.10 (90) {G0,W10,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y ), !
% 0.71/1.10 unequally_directed_lines( X, reverse_line( Y ) ), convergent_lines( X, Y
% 0.71/1.10 ) }.
% 0.71/1.10 (91) {G0,W12,D2,L3,V3,M3} { ! divides_points( Z, X, Y ), alpha1( X, Y, Z )
% 0.71/1.10 , alpha4( X, Y, Z ) }.
% 0.71/1.10 (92) {G0,W8,D2,L2,V3,M2} { ! alpha1( X, Y, Z ), divides_points( Z, X, Y )
% 0.71/1.10 }.
% 0.71/1.10 (93) {G0,W8,D2,L2,V3,M2} { ! alpha4( X, Y, Z ), divides_points( Z, X, Y )
% 0.71/1.10 }.
% 0.71/1.10 (94) {G0,W8,D3,L2,V3,M2} { ! alpha4( X, Y, Z ), left_apart_point( X,
% 0.71/1.10 reverse_line( Z ) ) }.
% 0.71/1.10 (95) {G0,W7,D2,L2,V3,M2} { ! alpha4( X, Y, Z ), left_apart_point( Y, Z )
% 0.71/1.10 }.
% 0.71/1.10 (96) {G0,W11,D3,L3,V3,M3} { ! left_apart_point( X, reverse_line( Z ) ), !
% 0.71/1.10 left_apart_point( Y, Z ), alpha4( X, Y, Z ) }.
% 0.71/1.10 (97) {G0,W7,D2,L2,V3,M2} { ! alpha1( X, Y, Z ), left_apart_point( X, Z )
% 0.71/1.10 }.
% 0.71/1.10 (98) {G0,W8,D3,L2,V3,M2} { ! alpha1( X, Y, Z ), left_apart_point( Y,
% 0.71/1.10 reverse_line( Z ) ) }.
% 0.71/1.10 (99) {G0,W11,D3,L3,V3,M3} { ! left_apart_point( X, Z ), ! left_apart_point
% 0.71/1.10 ( Y, reverse_line( Z ) ), alpha1( X, Y, Z ) }.
% 0.71/1.10 (100) {G0,W7,D2,L2,V3,M2} { ! before_on_line( X, Y, Z ), distinct_points(
% 0.71/1.10 Y, Z ) }.
% 0.71/1.10 (101) {G0,W8,D2,L2,V3,M2} { ! before_on_line( X, Y, Z ), alpha7( X, Y, Z )
% 0.71/1.10 }.
% 0.71/1.10 (102) {G0,W11,D2,L3,V3,M3} { ! distinct_points( Y, Z ), ! alpha7( X, Y, Z
% 0.71/1.10 ), before_on_line( X, Y, Z ) }.
% 0.71/1.10 (103) {G0,W7,D2,L2,V3,M2} { ! alpha7( X, Y, Z ), alpha2( X, Y ) }.
% 0.71/1.10 (104) {G0,W8,D2,L2,V3,M2} { ! alpha7( X, Y, Z ), alpha8( X, Y, Z ) }.
% 0.71/1.10 (105) {G0,W11,D2,L3,V3,M3} { ! alpha2( X, Y ), ! alpha8( X, Y, Z ), alpha7
% 0.71/1.10 ( X, Y, Z ) }.
% 0.71/1.10 (106) {G0,W7,D2,L2,V3,M2} { ! alpha8( X, Y, Z ), alpha5( X, Z ) }.
% 0.71/1.10 (107) {G0,W9,D3,L2,V3,M2} { ! alpha8( X, Y, Z ), !
% 0.71/1.10 unequally_directed_lines( X, line_connecting( Y, Z ) ) }.
% 0.71/1.10 (108) {G0,W12,D3,L3,V3,M3} { ! alpha5( X, Z ), unequally_directed_lines( X
% 0.71/1.10 , line_connecting( Y, Z ) ), alpha8( X, Y, Z ) }.
% 0.71/1.10 (109) {G0,W6,D2,L2,V2,M2} { ! alpha5( X, Y ), ! left_apart_point( Y, X )
% 0.71/1.10 }.
% 0.71/1.10 (110) {G0,W7,D3,L2,V2,M2} { ! alpha5( X, Y ), ! left_apart_point( Y,
% 0.71/1.10 reverse_line( X ) ) }.
% 0.71/1.10 (111) {G0,W10,D3,L3,V2,M3} { left_apart_point( Y, X ), left_apart_point( Y
% 0.71/1.10 , reverse_line( X ) ), alpha5( X, Y ) }.
% 0.71/1.10 (112) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), ! left_apart_point( Y, X )
% 0.71/1.10 }.
% 0.71/1.10 (113) {G0,W7,D3,L2,V2,M2} { ! alpha2( X, Y ), ! left_apart_point( Y,
% 0.71/1.10 reverse_line( X ) ) }.
% 0.71/1.10 (114) {G0,W10,D3,L3,V2,M3} { left_apart_point( Y, X ), left_apart_point( Y
% 0.71/1.10 , reverse_line( X ) ), alpha2( X, Y ) }.
% 0.71/1.10 (115) {G0,W15,D2,L3,V4,M3} { ! between_on_line( X, Y, Z, T ), alpha3( X, Y
% 0.71/1.10 , Z, T ), alpha6( X, Y, Z, T ) }.
% 0.71/1.10 (116) {G0,W10,D2,L2,V4,M2} { ! alpha3( X, Y, Z, T ), between_on_line( X, Y
% 0.71/1.10 , Z, T ) }.
% 0.71/1.10 (117) {G0,W10,D2,L2,V4,M2} { ! alpha6( X, Y, Z, T ), between_on_line( X, Y
% 0.71/1.10 , Z, T ) }.
% 0.71/1.10 (118) {G0,W9,D2,L2,V4,M2} { ! alpha6( X, Y, Z, T ), before_on_line( X, T,
% 0.71/1.10 Z ) }.
% 0.71/1.10 (119) {G0,W9,D2,L2,V4,M2} { ! alpha6( X, Y, Z, T ), before_on_line( X, Z,
% 0.71/1.10 Y ) }.
% 0.71/1.10 (120) {G0,W13,D2,L3,V4,M3} { ! before_on_line( X, T, Z ), ! before_on_line
% 0.71/1.10 ( X, Z, Y ), alpha6( X, Y, Z, T ) }.
% 0.71/1.10 (121) {G0,W9,D2,L2,V4,M2} { ! alpha3( X, Y, Z, T ), before_on_line( X, Y,
% 0.71/1.10 Z ) }.
% 0.71/1.10 (122) {G0,W9,D2,L2,V4,M2} { ! alpha3( X, Y, Z, T ), before_on_line( X, Z,
% 0.71/1.10 T ) }.
% 0.71/1.10 (123) {G0,W13,D2,L3,V4,M3} { ! before_on_line( X, Y, Z ), ! before_on_line
% 0.71/1.10 ( X, Z, T ), alpha3( X, Y, Z, T ) }.
% 0.71/1.10 (124) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 0.71/1.10 (125) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 0.71/1.10 , Z ), distinct_points( Y, Z ) }.
% 0.71/1.10 (126) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.71/1.10 (127) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X, Z
% 0.71/1.10 ), distinct_lines( Y, Z ) }.
% 0.71/1.10 (128) {G0,W3,D2,L1,V1,M1} { ! unequally_directed_lines( X, X ) }.
% 0.71/1.10 (129) {G0,W9,D2,L3,V3,M3} { ! unequally_directed_lines( X, Y ),
% 0.71/1.10 unequally_directed_lines( X, Z ), unequally_directed_lines( Y, Z ) }.
% 0.71/1.10 (130) {G0,W13,D3,L4,V3,M4} { ! unequally_directed_lines( X, Y ), !
% 0.71/1.10 unequally_directed_lines( X, reverse_line( Y ) ), alpha9( X, Z ),
% 0.71/1.10 unequally_directed_lines( Y, Z ) }.
% 0.71/1.10 (131) {G0,W14,D3,L4,V3,M4} { ! unequally_directed_lines( X, Y ), !
% 0.71/1.10 unequally_directed_lines( X, reverse_line( Y ) ), alpha9( X, Z ),
% 0.71/1.10 unequally_directed_lines( Y, reverse_line( Z ) ) }.
% 0.71/1.10 (132) {G0,W6,D2,L2,V2,M2} { ! alpha9( X, Y ), unequally_directed_lines( X
% 0.71/1.10 , Y ) }.
% 0.71/1.10 (133) {G0,W7,D3,L2,V2,M2} { ! alpha9( X, Y ), unequally_directed_lines( X
% 0.71/1.10 , reverse_line( Y ) ) }.
% 0.71/1.10 (134) {G0,W10,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y ), !
% 0.71/1.10 unequally_directed_lines( X, reverse_line( Y ) ), alpha9( X, Y ) }.
% 0.71/1.10 (135) {G0,W11,D3,L4,V2,M4} { ! line( X ), ! line( Y ),
% 0.71/1.10 unequally_directed_lines( X, Y ), unequally_directed_lines( X,
% 0.71/1.10 reverse_line( Y ) ) }.
% 0.71/1.10 (136) {G0,W14,D3,L4,V2,M4} { ! unequally_directed_lines( X, Y ), !
% 0.71/1.10 unequally_directed_lines( X, reverse_line( Y ) ), left_convergent_lines(
% 0.71/1.10 X, Y ), left_convergent_lines( X, reverse_line( Y ) ) }.
% 0.71/1.10 (137) {G0,W3,D2,L1,V2,M1} { ! left_apart_point( X, Y ) }.
% 0.71/1.10 (138) {G0,W4,D3,L1,V2,M1} { ! left_apart_point( X, reverse_line( Y ) ) }.
% 0.71/1.10 (139) {G0,W3,D2,L1,V2,M1} { ! left_convergent_lines( X, Y ) }.
% 0.71/1.10 (140) {G0,W4,D3,L1,V2,M1} { ! left_convergent_lines( X, reverse_line( Y )
% 0.71/1.10 ) }.
% 0.71/1.10 (141) {G0,W11,D3,L4,V2,M4} { ! point( X ), ! point( Y ), ! distinct_points
% 0.71/1.10 ( X, Y ), line( line_connecting( X, Y ) ) }.
% 0.71/1.10 (142) {G0,W15,D3,L5,V2,M5} { ! line( X ), ! line( Y ), !
% 0.71/1.10 unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.71/1.10 reverse_line( Y ) ), point( intersection_point( X, Y ) ) }.
% 0.71/1.10 (143) {G0,W8,D3,L3,V2,M3} { ! point( Y ), ! line( X ), line(
% 0.71/1.10 parallel_through_point( X, Y ) ) }.
% 0.71/1.10 (144) {G0,W5,D3,L2,V1,M2} { ! line( X ), line( reverse_line( X ) ) }.
% 0.71/1.10 (145) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.71/1.10 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 0.71/1.10 (146) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.71/1.10 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 0.71/1.10 (147) {G0,W12,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y ), !
% 0.71/1.10 unequally_directed_lines( X, reverse_line( Y ) ), ! apart_point_and_line
% 0.71/1.10 ( intersection_point( X, Y ), X ) }.
% 0.71/1.10 (148) {G0,W12,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y ), !
% 0.71/1.10 unequally_directed_lines( X, reverse_line( Y ) ), ! apart_point_and_line
% 0.71/1.10 ( intersection_point( X, Y ), Y ) }.
% 0.71/1.10 (149) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.71/1.10 parallel_through_point( Y, X ) ) }.
% 0.71/1.10 (150) {G0,W4,D3,L1,V1,M1} { ! distinct_lines( X, reverse_line( X ) ) }.
% 0.71/1.10 (151) {G0,W8,D4,L1,V2,M1} { ! unequally_directed_lines( line_connecting( X
% 0.71/1.10 , Y ), reverse_line( line_connecting( Y, X ) ) ) }.
% 0.71/1.10 (152) {G0,W5,D3,L1,V2,M1} { ! unequally_directed_lines(
% 0.71/1.10 parallel_through_point( Y, X ), Y ) }.
% 0.71/1.10 (153) {G0,W34,D3,L10,V4,M10} { ! distinct_points( X, Y ), ! distinct_lines
% 0.71/1.10 ( Z, T ), left_apart_point( X, Z ), left_apart_point( Y, Z ),
% 0.71/1.10 left_apart_point( X, T ), left_apart_point( Y, T ), left_apart_point( X,
% 0.71/1.10 reverse_line( Z ) ), left_apart_point( Y, reverse_line( Z ) ),
% 0.71/1.10 left_apart_point( X, reverse_line( T ) ), left_apart_point( Y,
% 0.71/1.10 reverse_line( T ) ) }.
% 0.71/1.10 (154) {G0,W14,D3,L4,V3,M4} { ! distinct_points( X, Y ), ! left_apart_point
% 0.71/1.10 ( X, Z ), left_apart_point( Y, Z ), left_convergent_lines(
% 0.71/1.10 line_connecting( X, Y ), Z ) }.
% 0.71/1.10 (155) {G0,W9,D2,L3,V3,M3} { ! left_apart_point( X, Y ), distinct_points( X
% 0.71/1.10 , Z ), left_apart_point( Z, Y ) }.
% 0.71/1.10 (156) {G0,W13,D3,L4,V3,M4} { ! left_apart_point( X, Y ), !
% 0.71/1.10 unequally_directed_lines( Y, Z ), distinct_lines( Y, Z ),
% 0.71/1.10 left_apart_point( X, reverse_line( Z ) ) }.
% 0.71/1.10 (157) {G0,W9,D2,L3,V3,M3} { ! left_convergent_lines( X, Y ),
% 0.71/1.10 unequally_directed_lines( Y, Z ), left_convergent_lines( X, Z ) }.
% 0.71/1.10 (158) {G0,W2,D2,L1,V0,M1} { line( skol1 ) }.
% 0.71/1.10 (159) {G0,W4,D3,L1,V0,M1} { ! unequally_directed_lines( skol1,
% 0.71/1.10 reverse_line( skol1 ) ) }.
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 Total Proof:
% 0.71/1.10
% 0.71/1.10 subsumption: (43) {G0,W3,D2,L1,V1,M1} I { ! unequally_directed_lines( X, X
% 0.71/1.10 ) }.
% 0.71/1.10 parent0: (128) {G0,W3,D2,L1,V1,M1} { ! unequally_directed_lines( X, X )
% 0.71/1.10 }.
% 0.71/1.10 substitution0:
% 0.71/1.10 X := X
% 0.71/1.10 end
% 0.71/1.10 permutation0:
% 0.71/1.10 0 ==> 0
% 0.71/1.10 end
% 0.71/1.10
% 0.71/1.10 subsumption: (50) {G0,W11,D3,L4,V2,M2} I { ! line( X ), ! line( Y ),
% 0.71/1.10 unequally_directed_lines( X, reverse_line( Y ) ),
% 0.71/1.10 unequally_directed_lines( X, Y ) }.
% 0.71/1.10 parent0: (135) {G0,W11,D3,L4,V2,M4} { ! line( X ), ! line( Y ),
% 0.71/1.10 unequally_directed_lines( X, Y ), unequally_directed_lines( X,
% 0.71/1.10 reverse_line( Y ) ) }.
% 0.71/1.10 substitution0:
% 0.71/1.10 X := X
% 0.71/1.10 Y := Y
% 0.71/1.10 end
% 0.71/1.10 permutation0:
% 0.71/1.10 0 ==> 0
% 0.71/1.10 1 ==> 1
% 0.71/1.10 2 ==> 3
% 0.71/1.10 3 ==> 2
% 0.71/1.10 end
% 0.71/1.10
% 0.71/1.10 subsumption: (67) {G0,W2,D2,L1,V0,M1} I { line( skol1 ) }.
% 0.71/1.10 parent0: (158) {G0,W2,D2,L1,V0,M1} { line( skol1 ) }.
% 0.71/1.10 substitution0:
% 0.71/1.10 end
% 0.71/1.10 permutation0:
% 0.71/1.10 0 ==> 0
% 0.71/1.10 end
% 0.71/1.10
% 0.71/1.10 subsumption: (68) {G0,W4,D3,L1,V0,M1} I { ! unequally_directed_lines( skol1
% 0.71/1.10 , reverse_line( skol1 ) ) }.
% 0.71/1.10 parent0: (159) {G0,W4,D3,L1,V0,M1} { ! unequally_directed_lines( skol1,
% 0.71/1.10 reverse_line( skol1 ) ) }.
% 0.71/1.10 substitution0:
% 0.71/1.10 end
% 0.71/1.10 permutation0:
% 0.71/1.10 0 ==> 0
% 0.71/1.10 end
% 0.71/1.10
% 0.71/1.10 factor: (238) {G0,W9,D3,L3,V1,M3} { ! line( X ), unequally_directed_lines
% 0.71/1.10 ( X, reverse_line( X ) ), unequally_directed_lines( X, X ) }.
% 0.71/1.10 parent0[0, 1]: (50) {G0,W11,D3,L4,V2,M2} I { ! line( X ), ! line( Y ),
% 0.71/1.10 unequally_directed_lines( X, reverse_line( Y ) ),
% 0.71/1.10 unequally_directed_lines( X, Y ) }.
% 0.71/1.10 substitution0:
% 0.71/1.10 X := X
% 0.71/1.10 Y := X
% 0.71/1.10 end
% 0.71/1.10
% 0.71/1.10 resolution: (239) {G1,W6,D3,L2,V1,M2} { ! line( X ),
% 0.71/1.10 unequally_directed_lines( X, reverse_line( X ) ) }.
% 0.71/1.10 parent0[0]: (43) {G0,W3,D2,L1,V1,M1} I { ! unequally_directed_lines( X, X )
% 0.71/1.10 }.
% 0.71/1.10 parent1[2]: (238) {G0,W9,D3,L3,V1,M3} { ! line( X ),
% 0.71/1.10 unequally_directed_lines( X, reverse_line( X ) ),
% 0.71/1.10 unequally_directed_lines( X, X ) }.
% 0.71/1.10 substitution0:
% 0.71/1.10 X := X
% 0.71/1.10 end
% 0.71/1.10 substitution1:
% 0.71/1.10 X := X
% 0.71/1.10 end
% 0.71/1.10
% 0.71/1.10 subsumption: (71) {G1,W6,D3,L2,V1,M1} F(50);r(43) { ! line( X ),
% 0.71/1.10 unequally_directed_lines( X, reverse_line( X ) ) }.
% 0.71/1.10 parent0: (239) {G1,W6,D3,L2,V1,M2} { ! line( X ), unequally_directed_lines
% 0.71/1.10 ( X, reverse_line( X ) ) }.
% 0.71/1.10 substitution0:
% 0.71/1.10 X := X
% 0.71/1.10 end
% 0.71/1.10 permutation0:
% 0.71/1.10 0 ==> 0
% 0.71/1.10 1 ==> 1
% 0.71/1.10 end
% 0.71/1.10
% 0.71/1.10 resolution: (240) {G1,W2,D2,L1,V0,M1} { ! line( skol1 ) }.
% 0.71/1.10 parent0[0]: (68) {G0,W4,D3,L1,V0,M1} I { ! unequally_directed_lines( skol1
% 0.71/1.10 , reverse_line( skol1 ) ) }.
% 0.71/1.10 parent1[1]: (71) {G1,W6,D3,L2,V1,M1} F(50);r(43) { ! line( X ),
% 0.71/1.10 unequally_directed_lines( X, reverse_line( X ) ) }.
% 0.71/1.10 substitution0:
% 0.71/1.10 end
% 0.71/1.10 substitution1:
% 0.71/1.10 X := skol1
% 0.71/1.10 end
% 0.71/1.10
% 0.71/1.10 resolution: (241) {G1,W0,D0,L0,V0,M0} { }.
% 0.71/1.10 parent0[0]: (240) {G1,W2,D2,L1,V0,M1} { ! line( skol1 ) }.
% 0.71/1.10 parent1[0]: (67) {G0,W2,D2,L1,V0,M1} I { line( skol1 ) }.
% 0.71/1.10 substitution0:
% 0.71/1.10 end
% 0.71/1.10 substitution1:
% 0.71/1.10 end
% 0.71/1.10
% 0.71/1.10 subsumption: (83) {G2,W0,D0,L0,V0,M0} R(71,68);r(67) { }.
% 0.71/1.10 parent0: (241) {G1,W0,D0,L0,V0,M0} { }.
% 0.71/1.10 substitution0:
% 0.71/1.10 end
% 0.71/1.10 permutation0:
% 0.71/1.10 end
% 0.71/1.10
% 0.71/1.10 Proof check complete!
% 0.71/1.10
% 0.71/1.10 Memory use:
% 0.71/1.10
% 0.71/1.10 space for terms: 2404
% 0.71/1.10 space for clauses: 4797
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 clauses generated: 112
% 0.71/1.10 clauses kept: 84
% 0.71/1.10 clauses selected: 22
% 0.71/1.10 clauses deleted: 6
% 0.71/1.10 clauses inuse deleted: 0
% 0.71/1.10
% 0.71/1.10 subsentry: 591
% 0.71/1.10 literals s-matched: 412
% 0.71/1.10 literals matched: 312
% 0.71/1.10 full subsumption: 115
% 0.71/1.10
% 0.71/1.10 checksum: 2089731868
% 0.71/1.10
% 0.71/1.10
% 0.71/1.10 Bliksem ended
%------------------------------------------------------------------------------