TSTP Solution File: GEO237+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO237+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n018.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 02:53:08 EDT 2022
% Result : Theorem 0.70s 1.07s
% Output : Refutation 0.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO237+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.07/0.12 % Command : bliksem %s
% 0.14/0.33 % Computer : n018.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % DateTime : Sat Jun 18 17:18:18 EDT 2022
% 0.14/0.33 % CPUTime :
% 0.70/1.07 *** allocated 10000 integers for termspace/termends
% 0.70/1.07 *** allocated 10000 integers for clauses
% 0.70/1.07 *** allocated 10000 integers for justifications
% 0.70/1.07 Bliksem 1.12
% 0.70/1.07
% 0.70/1.07
% 0.70/1.07 Automatic Strategy Selection
% 0.70/1.07
% 0.70/1.07
% 0.70/1.07 Clauses:
% 0.70/1.07
% 0.70/1.07 { ! apart_point_and_line( X, Y ), left_apart_point( X, Y ),
% 0.70/1.07 left_apart_point( X, reverse_line( Y ) ) }.
% 0.70/1.07 { ! left_apart_point( X, Y ), apart_point_and_line( X, Y ) }.
% 0.70/1.07 { ! left_apart_point( X, reverse_line( Y ) ), apart_point_and_line( X, Y )
% 0.70/1.07 }.
% 0.70/1.07 { ! convergent_lines( X, Y ), unequally_directed_lines( X, Y ) }.
% 0.70/1.07 { ! convergent_lines( X, Y ), unequally_directed_lines( X, reverse_line( Y
% 0.70/1.07 ) ) }.
% 0.70/1.07 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.70/1.07 reverse_line( Y ) ), convergent_lines( X, Y ) }.
% 0.70/1.07 { ! divides_points( Z, X, Y ), alpha1( X, Y, Z ), alpha4( X, Y, Z ) }.
% 0.70/1.07 { ! alpha1( X, Y, Z ), divides_points( Z, X, Y ) }.
% 0.70/1.07 { ! alpha4( X, Y, Z ), divides_points( Z, X, Y ) }.
% 0.70/1.07 { ! alpha4( X, Y, Z ), left_apart_point( X, reverse_line( Z ) ) }.
% 0.70/1.07 { ! alpha4( X, Y, Z ), left_apart_point( Y, Z ) }.
% 0.70/1.07 { ! left_apart_point( X, reverse_line( Z ) ), ! left_apart_point( Y, Z ),
% 0.70/1.07 alpha4( X, Y, Z ) }.
% 0.70/1.07 { ! alpha1( X, Y, Z ), left_apart_point( X, Z ) }.
% 0.70/1.07 { ! alpha1( X, Y, Z ), left_apart_point( Y, reverse_line( Z ) ) }.
% 0.70/1.07 { ! left_apart_point( X, Z ), ! left_apart_point( Y, reverse_line( Z ) ),
% 0.70/1.07 alpha1( X, Y, Z ) }.
% 0.70/1.07 { ! before_on_line( X, Y, Z ), distinct_points( Y, Z ) }.
% 0.70/1.07 { ! before_on_line( X, Y, Z ), alpha7( X, Y, Z ) }.
% 0.70/1.07 { ! distinct_points( Y, Z ), ! alpha7( X, Y, Z ), before_on_line( X, Y, Z )
% 0.70/1.07 }.
% 0.70/1.07 { ! alpha7( X, Y, Z ), alpha2( X, Y ) }.
% 0.70/1.07 { ! alpha7( X, Y, Z ), alpha8( X, Y, Z ) }.
% 0.70/1.07 { ! alpha2( X, Y ), ! alpha8( X, Y, Z ), alpha7( X, Y, Z ) }.
% 0.70/1.07 { ! alpha8( X, Y, Z ), alpha5( X, Z ) }.
% 0.70/1.07 { ! alpha8( X, Y, Z ), ! unequally_directed_lines( X, line_connecting( Y, Z
% 0.70/1.07 ) ) }.
% 0.70/1.07 { ! alpha5( X, Z ), unequally_directed_lines( X, line_connecting( Y, Z ) )
% 0.70/1.07 , alpha8( X, Y, Z ) }.
% 0.70/1.07 { ! alpha5( X, Y ), ! left_apart_point( Y, X ) }.
% 0.70/1.07 { ! alpha5( X, Y ), ! left_apart_point( Y, reverse_line( X ) ) }.
% 0.70/1.07 { left_apart_point( Y, X ), left_apart_point( Y, reverse_line( X ) ),
% 0.70/1.07 alpha5( X, Y ) }.
% 0.70/1.07 { ! alpha2( X, Y ), ! left_apart_point( Y, X ) }.
% 0.70/1.07 { ! alpha2( X, Y ), ! left_apart_point( Y, reverse_line( X ) ) }.
% 0.70/1.07 { left_apart_point( Y, X ), left_apart_point( Y, reverse_line( X ) ),
% 0.70/1.07 alpha2( X, Y ) }.
% 0.70/1.07 { ! between_on_line( X, Y, Z, T ), alpha3( X, Y, Z, T ), alpha6( X, Y, Z, T
% 0.70/1.07 ) }.
% 0.70/1.07 { ! alpha3( X, Y, Z, T ), between_on_line( X, Y, Z, T ) }.
% 0.70/1.07 { ! alpha6( X, Y, Z, T ), between_on_line( X, Y, Z, T ) }.
% 0.70/1.07 { ! alpha6( X, Y, Z, T ), before_on_line( X, T, Z ) }.
% 0.70/1.07 { ! alpha6( X, Y, Z, T ), before_on_line( X, Z, Y ) }.
% 0.70/1.07 { ! before_on_line( X, T, Z ), ! before_on_line( X, Z, Y ), alpha6( X, Y, Z
% 0.70/1.07 , T ) }.
% 0.70/1.07 { ! alpha3( X, Y, Z, T ), before_on_line( X, Y, Z ) }.
% 0.70/1.07 { ! alpha3( X, Y, Z, T ), before_on_line( X, Z, T ) }.
% 0.70/1.07 { ! before_on_line( X, Y, Z ), ! before_on_line( X, Z, T ), alpha3( X, Y, Z
% 0.70/1.07 , T ) }.
% 0.70/1.07 { ! distinct_points( X, X ) }.
% 0.70/1.07 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 0.70/1.07 ) }.
% 0.70/1.07 { ! distinct_lines( X, X ) }.
% 0.70/1.07 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.70/1.07 }.
% 0.70/1.07 { ! unequally_directed_lines( X, X ) }.
% 0.70/1.07 { ! unequally_directed_lines( X, Y ), unequally_directed_lines( X, Z ),
% 0.70/1.07 unequally_directed_lines( Y, Z ) }.
% 0.70/1.07 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.70/1.07 reverse_line( Y ) ), alpha9( X, Z ), unequally_directed_lines( Y, Z ) }.
% 0.70/1.07 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.70/1.07 reverse_line( Y ) ), alpha9( X, Z ), unequally_directed_lines( Y,
% 0.70/1.07 reverse_line( Z ) ) }.
% 0.70/1.07 { ! alpha9( X, Y ), unequally_directed_lines( X, Y ) }.
% 0.70/1.07 { ! alpha9( X, Y ), unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.70/1.07 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.70/1.07 reverse_line( Y ) ), alpha9( X, Y ) }.
% 0.70/1.07 { ! line( X ), ! line( Y ), unequally_directed_lines( X, Y ),
% 0.70/1.07 unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.70/1.07 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.70/1.07 reverse_line( Y ) ), left_convergent_lines( X, Y ), left_convergent_lines
% 0.70/1.07 ( X, reverse_line( Y ) ) }.
% 0.70/1.07 { ! left_apart_point( X, Y ) }.
% 0.70/1.07 { ! left_apart_point( X, reverse_line( Y ) ) }.
% 0.70/1.07 { ! left_convergent_lines( X, Y ) }.
% 0.70/1.07 { ! left_convergent_lines( X, reverse_line( Y ) ) }.
% 0.70/1.07 { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line(
% 0.70/1.07 line_connecting( X, Y ) ) }.
% 0.70/1.07 { ! line( X ), ! line( Y ), ! unequally_directed_lines( X, Y ), !
% 0.70/1.07 unequally_directed_lines( X, reverse_line( Y ) ), point(
% 0.70/1.07 intersection_point( X, Y ) ) }.
% 0.70/1.07 { ! point( Y ), ! line( X ), line( parallel_through_point( X, Y ) ) }.
% 0.70/1.07 { ! line( X ), line( reverse_line( X ) ) }.
% 0.70/1.07 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 0.70/1.07 , Y ) ) }.
% 0.70/1.07 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 0.70/1.07 , Y ) ) }.
% 0.70/1.07 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.70/1.07 reverse_line( Y ) ), ! apart_point_and_line( intersection_point( X, Y ),
% 0.70/1.07 X ) }.
% 0.70/1.07 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.70/1.07 reverse_line( Y ) ), ! apart_point_and_line( intersection_point( X, Y ),
% 0.70/1.07 Y ) }.
% 0.70/1.07 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 0.70/1.07 { ! distinct_lines( X, reverse_line( X ) ) }.
% 0.70/1.07 { ! unequally_directed_lines( line_connecting( X, Y ), reverse_line(
% 0.70/1.07 line_connecting( Y, X ) ) ) }.
% 0.70/1.07 { ! unequally_directed_lines( parallel_through_point( Y, X ), Y ) }.
% 0.70/1.07 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), left_apart_point( X
% 0.70/1.07 , Z ), left_apart_point( Y, Z ), left_apart_point( X, T ),
% 0.70/1.07 left_apart_point( Y, T ), left_apart_point( X, reverse_line( Z ) ),
% 0.70/1.07 left_apart_point( Y, reverse_line( Z ) ), left_apart_point( X,
% 0.70/1.07 reverse_line( T ) ), left_apart_point( Y, reverse_line( T ) ) }.
% 0.70/1.07 { ! distinct_points( X, Y ), ! left_apart_point( X, Z ), left_apart_point(
% 0.70/1.07 Y, Z ), left_convergent_lines( line_connecting( X, Y ), Z ) }.
% 0.70/1.07 { ! left_apart_point( X, Y ), distinct_points( X, Z ), left_apart_point( Z
% 0.70/1.07 , Y ) }.
% 0.70/1.07 { ! left_apart_point( X, Y ), ! unequally_directed_lines( Y, Z ),
% 0.70/1.07 distinct_lines( Y, Z ), left_apart_point( X, reverse_line( Z ) ) }.
% 0.70/1.07 { ! left_convergent_lines( X, Y ), unequally_directed_lines( Y, Z ),
% 0.70/1.07 left_convergent_lines( X, Z ) }.
% 0.70/1.07 { apart_point_and_line( skol1, skol2 ) }.
% 0.70/1.07 { divides_points( skol2, skol3, skol4 ) }.
% 0.70/1.07 { ! divides_points( skol2, skol3, skol1 ) }.
% 0.70/1.07 { ! divides_points( skol2, skol4, skol1 ) }.
% 0.70/1.07
% 0.70/1.07 percentage equality = 0.000000, percentage horn = 0.802817
% 0.70/1.07 This a non-horn, non-equality problem
% 0.70/1.07
% 0.70/1.07
% 0.70/1.07 Options Used:
% 0.70/1.07
% 0.70/1.07 useres = 1
% 0.70/1.07 useparamod = 0
% 0.70/1.07 useeqrefl = 0
% 0.70/1.07 useeqfact = 0
% 0.70/1.07 usefactor = 1
% 0.70/1.07 usesimpsplitting = 0
% 0.70/1.07 usesimpdemod = 0
% 0.70/1.07 usesimpres = 3
% 0.70/1.07
% 0.70/1.07 resimpinuse = 1000
% 0.70/1.07 resimpclauses = 20000
% 0.70/1.07 substype = standard
% 0.70/1.07 backwardsubs = 1
% 0.70/1.07 selectoldest = 5
% 0.70/1.07
% 0.70/1.07 litorderings [0] = split
% 0.70/1.07 litorderings [1] = liftord
% 0.70/1.07
% 0.70/1.07 termordering = none
% 0.70/1.07
% 0.70/1.07 litapriori = 1
% 0.70/1.07 termapriori = 0
% 0.70/1.07 litaposteriori = 0
% 0.70/1.07 termaposteriori = 0
% 0.70/1.07 demodaposteriori = 0
% 0.70/1.07 ordereqreflfact = 0
% 0.70/1.07
% 0.70/1.07 litselect = none
% 0.70/1.07
% 0.70/1.07 maxweight = 15
% 0.70/1.07 maxdepth = 30000
% 0.70/1.07 maxlength = 115
% 0.70/1.07 maxnrvars = 195
% 0.70/1.07 excuselevel = 1
% 0.70/1.07 increasemaxweight = 1
% 0.70/1.07
% 0.70/1.07 maxselected = 10000000
% 0.70/1.07 maxnrclauses = 10000000
% 0.70/1.07
% 0.70/1.07 showgenerated = 0
% 0.70/1.07 showkept = 0
% 0.70/1.07 showselected = 0
% 0.70/1.07 showdeleted = 0
% 0.70/1.07 showresimp = 1
% 0.70/1.07 showstatus = 2000
% 0.70/1.07
% 0.70/1.07 prologoutput = 0
% 0.70/1.07 nrgoals = 5000000
% 0.70/1.07 totalproof = 1
% 0.70/1.07
% 0.70/1.07 Symbols occurring in the translation:
% 0.70/1.07
% 0.70/1.07 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.70/1.07 . [1, 2] (w:1, o:24, a:1, s:1, b:0),
% 0.70/1.07 ! [4, 1] (w:0, o:16, a:1, s:1, b:0),
% 0.70/1.07 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.70/1.07 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.70/1.07 apart_point_and_line [37, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.70/1.07 left_apart_point [38, 2] (w:1, o:49, a:1, s:1, b:0),
% 0.70/1.07 reverse_line [39, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.70/1.07 convergent_lines [41, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.70/1.07 unequally_directed_lines [42, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.70/1.07 divides_points [44, 3] (w:1, o:61, a:1, s:1, b:0),
% 0.70/1.07 before_on_line [45, 3] (w:1, o:66, a:1, s:1, b:0),
% 0.70/1.07 distinct_points [46, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.70/1.07 line_connecting [47, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.70/1.07 between_on_line [49, 4] (w:1, o:69, a:1, s:1, b:0),
% 0.70/1.07 distinct_lines [50, 2] (w:1, o:54, a:1, s:1, b:0),
% 0.70/1.07 line [52, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.70/1.07 left_convergent_lines [53, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.70/1.07 point [54, 1] (w:1, o:23, a:1, s:1, b:0),
% 0.70/1.07 intersection_point [55, 2] (w:1, o:56, a:1, s:1, b:0),
% 0.70/1.07 parallel_through_point [56, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.70/1.07 alpha1 [57, 3] (w:1, o:62, a:1, s:1, b:0),
% 0.70/1.07 alpha2 [58, 2] (w:1, o:58, a:1, s:1, b:0),
% 0.70/1.07 alpha3 [59, 4] (w:1, o:67, a:1, s:1, b:0),
% 0.70/1.07 alpha4 [60, 3] (w:1, o:63, a:1, s:1, b:0),
% 0.70/1.07 alpha5 [61, 2] (w:1, o:59, a:1, s:1, b:0),
% 0.70/1.07 alpha6 [62, 4] (w:1, o:68, a:1, s:1, b:0),
% 0.70/1.07 alpha7 [63, 3] (w:1, o:64, a:1, s:1, b:0),
% 0.70/1.07 alpha8 [64, 3] (w:1, o:65, a:1, s:1, b:0),
% 0.70/1.07 alpha9 [65, 2] (w:1, o:60, a:1, s:1, b:0),
% 0.70/1.07 skol1 [66, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.70/1.07 skol2 [67, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.70/1.07 skol3 [68, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.70/1.07 skol4 [69, 0] (w:1, o:15, a:1, s:1, b:0).
% 0.70/1.07
% 0.70/1.07
% 0.70/1.07 Starting Search:
% 0.70/1.07
% 0.70/1.07
% 0.70/1.07 Bliksems!, er is een bewijs:
% 0.70/1.07 % SZS status Theorem
% 0.70/1.07 % SZS output start Refutation
% 0.70/1.07
% 0.70/1.07 (0) {G0,W10,D3,L3,V2,M2} I { ! apart_point_and_line( X, Y ),
% 0.70/1.07 left_apart_point( X, reverse_line( Y ) ), left_apart_point( X, Y ) }.
% 0.70/1.07 (52) {G0,W3,D2,L1,V2,M1} I { ! left_apart_point( X, Y ) }.
% 0.70/1.07 (67) {G0,W3,D2,L1,V0,M1} I { apart_point_and_line( skol1, skol2 ) }.
% 0.70/1.07 (74) {G1,W3,D2,L1,V2,M1} S(0);r(52);r(52) { ! apart_point_and_line( X, Y )
% 0.70/1.07 }.
% 0.70/1.07 (75) {G2,W0,D0,L0,V0,M0} S(67);r(74) { }.
% 0.70/1.07
% 0.70/1.07
% 0.70/1.07 % SZS output end Refutation
% 0.70/1.07 found a proof!
% 0.70/1.07
% 0.70/1.07
% 0.70/1.07 Unprocessed initial clauses:
% 0.70/1.07
% 0.70/1.07 (77) {G0,W10,D3,L3,V2,M3} { ! apart_point_and_line( X, Y ),
% 0.70/1.07 left_apart_point( X, Y ), left_apart_point( X, reverse_line( Y ) ) }.
% 0.70/1.07 (78) {G0,W6,D2,L2,V2,M2} { ! left_apart_point( X, Y ),
% 0.70/1.07 apart_point_and_line( X, Y ) }.
% 0.70/1.07 (79) {G0,W7,D3,L2,V2,M2} { ! left_apart_point( X, reverse_line( Y ) ),
% 0.70/1.07 apart_point_and_line( X, Y ) }.
% 0.70/1.07 (80) {G0,W6,D2,L2,V2,M2} { ! convergent_lines( X, Y ),
% 0.70/1.07 unequally_directed_lines( X, Y ) }.
% 0.70/1.07 (81) {G0,W7,D3,L2,V2,M2} { ! convergent_lines( X, Y ),
% 0.70/1.07 unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.70/1.07 (82) {G0,W10,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y ), !
% 0.70/1.07 unequally_directed_lines( X, reverse_line( Y ) ), convergent_lines( X, Y
% 0.70/1.07 ) }.
% 0.70/1.07 (83) {G0,W12,D2,L3,V3,M3} { ! divides_points( Z, X, Y ), alpha1( X, Y, Z )
% 0.70/1.07 , alpha4( X, Y, Z ) }.
% 0.70/1.07 (84) {G0,W8,D2,L2,V3,M2} { ! alpha1( X, Y, Z ), divides_points( Z, X, Y )
% 0.70/1.07 }.
% 0.70/1.07 (85) {G0,W8,D2,L2,V3,M2} { ! alpha4( X, Y, Z ), divides_points( Z, X, Y )
% 0.70/1.07 }.
% 0.70/1.07 (86) {G0,W8,D3,L2,V3,M2} { ! alpha4( X, Y, Z ), left_apart_point( X,
% 0.70/1.07 reverse_line( Z ) ) }.
% 0.70/1.07 (87) {G0,W7,D2,L2,V3,M2} { ! alpha4( X, Y, Z ), left_apart_point( Y, Z )
% 0.70/1.07 }.
% 0.70/1.07 (88) {G0,W11,D3,L3,V3,M3} { ! left_apart_point( X, reverse_line( Z ) ), !
% 0.70/1.07 left_apart_point( Y, Z ), alpha4( X, Y, Z ) }.
% 0.70/1.07 (89) {G0,W7,D2,L2,V3,M2} { ! alpha1( X, Y, Z ), left_apart_point( X, Z )
% 0.70/1.07 }.
% 0.70/1.07 (90) {G0,W8,D3,L2,V3,M2} { ! alpha1( X, Y, Z ), left_apart_point( Y,
% 0.70/1.07 reverse_line( Z ) ) }.
% 0.70/1.07 (91) {G0,W11,D3,L3,V3,M3} { ! left_apart_point( X, Z ), ! left_apart_point
% 0.70/1.07 ( Y, reverse_line( Z ) ), alpha1( X, Y, Z ) }.
% 0.70/1.07 (92) {G0,W7,D2,L2,V3,M2} { ! before_on_line( X, Y, Z ), distinct_points( Y
% 0.70/1.07 , Z ) }.
% 0.70/1.07 (93) {G0,W8,D2,L2,V3,M2} { ! before_on_line( X, Y, Z ), alpha7( X, Y, Z )
% 0.70/1.07 }.
% 0.70/1.07 (94) {G0,W11,D2,L3,V3,M3} { ! distinct_points( Y, Z ), ! alpha7( X, Y, Z )
% 0.70/1.07 , before_on_line( X, Y, Z ) }.
% 0.70/1.07 (95) {G0,W7,D2,L2,V3,M2} { ! alpha7( X, Y, Z ), alpha2( X, Y ) }.
% 0.70/1.07 (96) {G0,W8,D2,L2,V3,M2} { ! alpha7( X, Y, Z ), alpha8( X, Y, Z ) }.
% 0.70/1.07 (97) {G0,W11,D2,L3,V3,M3} { ! alpha2( X, Y ), ! alpha8( X, Y, Z ), alpha7
% 0.70/1.07 ( X, Y, Z ) }.
% 0.70/1.07 (98) {G0,W7,D2,L2,V3,M2} { ! alpha8( X, Y, Z ), alpha5( X, Z ) }.
% 0.70/1.07 (99) {G0,W9,D3,L2,V3,M2} { ! alpha8( X, Y, Z ), ! unequally_directed_lines
% 0.70/1.07 ( X, line_connecting( Y, Z ) ) }.
% 0.70/1.07 (100) {G0,W12,D3,L3,V3,M3} { ! alpha5( X, Z ), unequally_directed_lines( X
% 0.70/1.07 , line_connecting( Y, Z ) ), alpha8( X, Y, Z ) }.
% 0.70/1.07 (101) {G0,W6,D2,L2,V2,M2} { ! alpha5( X, Y ), ! left_apart_point( Y, X )
% 0.70/1.07 }.
% 0.70/1.07 (102) {G0,W7,D3,L2,V2,M2} { ! alpha5( X, Y ), ! left_apart_point( Y,
% 0.70/1.07 reverse_line( X ) ) }.
% 0.70/1.07 (103) {G0,W10,D3,L3,V2,M3} { left_apart_point( Y, X ), left_apart_point( Y
% 0.70/1.07 , reverse_line( X ) ), alpha5( X, Y ) }.
% 0.70/1.07 (104) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), ! left_apart_point( Y, X )
% 0.70/1.07 }.
% 0.70/1.07 (105) {G0,W7,D3,L2,V2,M2} { ! alpha2( X, Y ), ! left_apart_point( Y,
% 0.70/1.07 reverse_line( X ) ) }.
% 0.70/1.07 (106) {G0,W10,D3,L3,V2,M3} { left_apart_point( Y, X ), left_apart_point( Y
% 0.70/1.07 , reverse_line( X ) ), alpha2( X, Y ) }.
% 0.70/1.07 (107) {G0,W15,D2,L3,V4,M3} { ! between_on_line( X, Y, Z, T ), alpha3( X, Y
% 0.70/1.07 , Z, T ), alpha6( X, Y, Z, T ) }.
% 0.70/1.07 (108) {G0,W10,D2,L2,V4,M2} { ! alpha3( X, Y, Z, T ), between_on_line( X, Y
% 0.70/1.07 , Z, T ) }.
% 0.70/1.07 (109) {G0,W10,D2,L2,V4,M2} { ! alpha6( X, Y, Z, T ), between_on_line( X, Y
% 0.70/1.07 , Z, T ) }.
% 0.70/1.07 (110) {G0,W9,D2,L2,V4,M2} { ! alpha6( X, Y, Z, T ), before_on_line( X, T,
% 0.70/1.07 Z ) }.
% 0.70/1.07 (111) {G0,W9,D2,L2,V4,M2} { ! alpha6( X, Y, Z, T ), before_on_line( X, Z,
% 0.70/1.07 Y ) }.
% 0.70/1.07 (112) {G0,W13,D2,L3,V4,M3} { ! before_on_line( X, T, Z ), ! before_on_line
% 0.70/1.07 ( X, Z, Y ), alpha6( X, Y, Z, T ) }.
% 0.70/1.07 (113) {G0,W9,D2,L2,V4,M2} { ! alpha3( X, Y, Z, T ), before_on_line( X, Y,
% 0.70/1.07 Z ) }.
% 0.70/1.07 (114) {G0,W9,D2,L2,V4,M2} { ! alpha3( X, Y, Z, T ), before_on_line( X, Z,
% 0.70/1.07 T ) }.
% 0.70/1.07 (115) {G0,W13,D2,L3,V4,M3} { ! before_on_line( X, Y, Z ), ! before_on_line
% 0.70/1.07 ( X, Z, T ), alpha3( X, Y, Z, T ) }.
% 0.70/1.07 (116) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 0.70/1.07 (117) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 0.70/1.07 , Z ), distinct_points( Y, Z ) }.
% 0.70/1.07 (118) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.70/1.07 (119) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X, Z
% 0.70/1.07 ), distinct_lines( Y, Z ) }.
% 0.70/1.07 (120) {G0,W3,D2,L1,V1,M1} { ! unequally_directed_lines( X, X ) }.
% 0.70/1.07 (121) {G0,W9,D2,L3,V3,M3} { ! unequally_directed_lines( X, Y ),
% 0.70/1.07 unequally_directed_lines( X, Z ), unequally_directed_lines( Y, Z ) }.
% 0.70/1.07 (122) {G0,W13,D3,L4,V3,M4} { ! unequally_directed_lines( X, Y ), !
% 0.70/1.07 unequally_directed_lines( X, reverse_line( Y ) ), alpha9( X, Z ),
% 0.70/1.07 unequally_directed_lines( Y, Z ) }.
% 0.70/1.07 (123) {G0,W14,D3,L4,V3,M4} { ! unequally_directed_lines( X, Y ), !
% 0.70/1.07 unequally_directed_lines( X, reverse_line( Y ) ), alpha9( X, Z ),
% 0.70/1.07 unequally_directed_lines( Y, reverse_line( Z ) ) }.
% 0.70/1.07 (124) {G0,W6,D2,L2,V2,M2} { ! alpha9( X, Y ), unequally_directed_lines( X
% 0.70/1.07 , Y ) }.
% 0.70/1.07 (125) {G0,W7,D3,L2,V2,M2} { ! alpha9( X, Y ), unequally_directed_lines( X
% 0.70/1.07 , reverse_line( Y ) ) }.
% 0.70/1.07 (126) {G0,W10,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y ), !
% 0.70/1.07 unequally_directed_lines( X, reverse_line( Y ) ), alpha9( X, Y ) }.
% 0.70/1.07 (127) {G0,W11,D3,L4,V2,M4} { ! line( X ), ! line( Y ),
% 0.70/1.07 unequally_directed_lines( X, Y ), unequally_directed_lines( X,
% 0.70/1.07 reverse_line( Y ) ) }.
% 0.70/1.07 (128) {G0,W14,D3,L4,V2,M4} { ! unequally_directed_lines( X, Y ), !
% 0.70/1.07 unequally_directed_lines( X, reverse_line( Y ) ), left_convergent_lines(
% 0.70/1.07 X, Y ), left_convergent_lines( X, reverse_line( Y ) ) }.
% 0.70/1.07 (129) {G0,W3,D2,L1,V2,M1} { ! left_apart_point( X, Y ) }.
% 0.70/1.07 (130) {G0,W4,D3,L1,V2,M1} { ! left_apart_point( X, reverse_line( Y ) ) }.
% 0.70/1.07 (131) {G0,W3,D2,L1,V2,M1} { ! left_convergent_lines( X, Y ) }.
% 0.70/1.07 (132) {G0,W4,D3,L1,V2,M1} { ! left_convergent_lines( X, reverse_line( Y )
% 0.70/1.07 ) }.
% 0.70/1.07 (133) {G0,W11,D3,L4,V2,M4} { ! point( X ), ! point( Y ), ! distinct_points
% 0.70/1.07 ( X, Y ), line( line_connecting( X, Y ) ) }.
% 0.70/1.07 (134) {G0,W15,D3,L5,V2,M5} { ! line( X ), ! line( Y ), !
% 0.70/1.07 unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.70/1.07 reverse_line( Y ) ), point( intersection_point( X, Y ) ) }.
% 0.70/1.07 (135) {G0,W8,D3,L3,V2,M3} { ! point( Y ), ! line( X ), line(
% 0.70/1.07 parallel_through_point( X, Y ) ) }.
% 0.70/1.07 (136) {G0,W5,D3,L2,V1,M2} { ! line( X ), line( reverse_line( X ) ) }.
% 0.70/1.07 (137) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.70/1.07 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 0.70/1.07 (138) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.70/1.07 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 0.70/1.07 (139) {G0,W12,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y ), !
% 0.70/1.07 unequally_directed_lines( X, reverse_line( Y ) ), ! apart_point_and_line
% 0.70/1.08 ( intersection_point( X, Y ), X ) }.
% 0.70/1.08 (140) {G0,W12,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y ), !
% 0.70/1.08 unequally_directed_lines( X, reverse_line( Y ) ), ! apart_point_and_line
% 0.70/1.08 ( intersection_point( X, Y ), Y ) }.
% 0.70/1.08 (141) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.70/1.08 parallel_through_point( Y, X ) ) }.
% 0.70/1.08 (142) {G0,W4,D3,L1,V1,M1} { ! distinct_lines( X, reverse_line( X ) ) }.
% 0.70/1.08 (143) {G0,W8,D4,L1,V2,M1} { ! unequally_directed_lines( line_connecting( X
% 0.70/1.08 , Y ), reverse_line( line_connecting( Y, X ) ) ) }.
% 0.70/1.08 (144) {G0,W5,D3,L1,V2,M1} { ! unequally_directed_lines(
% 0.70/1.08 parallel_through_point( Y, X ), Y ) }.
% 0.70/1.08 (145) {G0,W34,D3,L10,V4,M10} { ! distinct_points( X, Y ), ! distinct_lines
% 0.70/1.08 ( Z, T ), left_apart_point( X, Z ), left_apart_point( Y, Z ),
% 0.70/1.08 left_apart_point( X, T ), left_apart_point( Y, T ), left_apart_point( X,
% 0.70/1.08 reverse_line( Z ) ), left_apart_point( Y, reverse_line( Z ) ),
% 0.70/1.08 left_apart_point( X, reverse_line( T ) ), left_apart_point( Y,
% 0.70/1.08 reverse_line( T ) ) }.
% 0.70/1.08 (146) {G0,W14,D3,L4,V3,M4} { ! distinct_points( X, Y ), ! left_apart_point
% 0.70/1.08 ( X, Z ), left_apart_point( Y, Z ), left_convergent_lines(
% 0.70/1.08 line_connecting( X, Y ), Z ) }.
% 0.70/1.08 (147) {G0,W9,D2,L3,V3,M3} { ! left_apart_point( X, Y ), distinct_points( X
% 0.70/1.08 , Z ), left_apart_point( Z, Y ) }.
% 0.70/1.08 (148) {G0,W13,D3,L4,V3,M4} { ! left_apart_point( X, Y ), !
% 0.70/1.08 unequally_directed_lines( Y, Z ), distinct_lines( Y, Z ),
% 0.70/1.08 left_apart_point( X, reverse_line( Z ) ) }.
% 0.70/1.08 (149) {G0,W9,D2,L3,V3,M3} { ! left_convergent_lines( X, Y ),
% 0.70/1.08 unequally_directed_lines( Y, Z ), left_convergent_lines( X, Z ) }.
% 0.70/1.08 (150) {G0,W3,D2,L1,V0,M1} { apart_point_and_line( skol1, skol2 ) }.
% 0.70/1.08 (151) {G0,W4,D2,L1,V0,M1} { divides_points( skol2, skol3, skol4 ) }.
% 0.70/1.08 (152) {G0,W4,D2,L1,V0,M1} { ! divides_points( skol2, skol3, skol1 ) }.
% 0.70/1.08 (153) {G0,W4,D2,L1,V0,M1} { ! divides_points( skol2, skol4, skol1 ) }.
% 0.70/1.08
% 0.70/1.08
% 0.70/1.08 Total Proof:
% 0.70/1.08
% 0.70/1.08 subsumption: (0) {G0,W10,D3,L3,V2,M2} I { ! apart_point_and_line( X, Y ),
% 0.70/1.08 left_apart_point( X, reverse_line( Y ) ), left_apart_point( X, Y ) }.
% 0.70/1.08 parent0: (77) {G0,W10,D3,L3,V2,M3} { ! apart_point_and_line( X, Y ),
% 0.70/1.08 left_apart_point( X, Y ), left_apart_point( X, reverse_line( Y ) ) }.
% 0.70/1.08 substitution0:
% 0.70/1.08 X := X
% 0.70/1.08 Y := Y
% 0.70/1.08 end
% 0.70/1.08 permutation0:
% 0.70/1.08 0 ==> 0
% 0.70/1.08 1 ==> 2
% 0.70/1.08 2 ==> 1
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 subsumption: (52) {G0,W3,D2,L1,V2,M1} I { ! left_apart_point( X, Y ) }.
% 0.70/1.08 parent0: (129) {G0,W3,D2,L1,V2,M1} { ! left_apart_point( X, Y ) }.
% 0.70/1.08 substitution0:
% 0.70/1.08 X := X
% 0.70/1.08 Y := Y
% 0.70/1.08 end
% 0.70/1.08 permutation0:
% 0.70/1.08 0 ==> 0
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 subsumption: (67) {G0,W3,D2,L1,V0,M1} I { apart_point_and_line( skol1,
% 0.70/1.08 skol2 ) }.
% 0.70/1.08 parent0: (150) {G0,W3,D2,L1,V0,M1} { apart_point_and_line( skol1, skol2 )
% 0.70/1.08 }.
% 0.70/1.08 substitution0:
% 0.70/1.08 end
% 0.70/1.08 permutation0:
% 0.70/1.08 0 ==> 0
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 resolution: (194) {G1,W6,D2,L2,V2,M2} { ! apart_point_and_line( X, Y ),
% 0.70/1.08 left_apart_point( X, Y ) }.
% 0.70/1.08 parent0[0]: (52) {G0,W3,D2,L1,V2,M1} I { ! left_apart_point( X, Y ) }.
% 0.70/1.08 parent1[1]: (0) {G0,W10,D3,L3,V2,M2} I { ! apart_point_and_line( X, Y ),
% 0.70/1.08 left_apart_point( X, reverse_line( Y ) ), left_apart_point( X, Y ) }.
% 0.70/1.08 substitution0:
% 0.70/1.08 X := X
% 0.70/1.08 Y := reverse_line( Y )
% 0.70/1.08 end
% 0.70/1.08 substitution1:
% 0.70/1.08 X := X
% 0.70/1.08 Y := Y
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 resolution: (196) {G1,W3,D2,L1,V2,M1} { ! apart_point_and_line( X, Y ) }.
% 0.70/1.08 parent0[0]: (52) {G0,W3,D2,L1,V2,M1} I { ! left_apart_point( X, Y ) }.
% 0.70/1.08 parent1[1]: (194) {G1,W6,D2,L2,V2,M2} { ! apart_point_and_line( X, Y ),
% 0.70/1.08 left_apart_point( X, Y ) }.
% 0.70/1.08 substitution0:
% 0.70/1.08 X := X
% 0.70/1.08 Y := Y
% 0.70/1.08 end
% 0.70/1.08 substitution1:
% 0.70/1.08 X := X
% 0.70/1.08 Y := Y
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 subsumption: (74) {G1,W3,D2,L1,V2,M1} S(0);r(52);r(52) { !
% 0.70/1.08 apart_point_and_line( X, Y ) }.
% 0.70/1.08 parent0: (196) {G1,W3,D2,L1,V2,M1} { ! apart_point_and_line( X, Y ) }.
% 0.70/1.08 substitution0:
% 0.70/1.08 X := X
% 0.70/1.08 Y := Y
% 0.70/1.08 end
% 0.70/1.08 permutation0:
% 0.70/1.08 0 ==> 0
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 resolution: (197) {G1,W0,D0,L0,V0,M0} { }.
% 0.70/1.08 parent0[0]: (74) {G1,W3,D2,L1,V2,M1} S(0);r(52);r(52) { !
% 0.70/1.08 apart_point_and_line( X, Y ) }.
% 0.70/1.08 parent1[0]: (67) {G0,W3,D2,L1,V0,M1} I { apart_point_and_line( skol1, skol2
% 0.70/1.08 ) }.
% 0.70/1.08 substitution0:
% 0.70/1.08 X := skol1
% 0.70/1.08 Y := skol2
% 0.70/1.08 end
% 0.70/1.08 substitution1:
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 subsumption: (75) {G2,W0,D0,L0,V0,M0} S(67);r(74) { }.
% 0.70/1.08 parent0: (197) {G1,W0,D0,L0,V0,M0} { }.
% 0.70/1.08 substitution0:
% 0.70/1.08 end
% 0.70/1.08 permutation0:
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 Proof check complete!
% 0.70/1.08
% 0.70/1.08 Memory use:
% 0.70/1.08
% 0.70/1.08 space for terms: 2393
% 0.70/1.08 space for clauses: 4379
% 0.70/1.08
% 0.70/1.08
% 0.70/1.08 clauses generated: 102
% 0.70/1.08 clauses kept: 76
% 0.70/1.08 clauses selected: 6
% 0.70/1.08 clauses deleted: 2
% 0.70/1.08 clauses inuse deleted: 0
% 0.70/1.08
% 0.70/1.08 subsentry: 307
% 0.70/1.08 literals s-matched: 216
% 0.70/1.08 literals matched: 166
% 0.70/1.08 full subsumption: 60
% 0.70/1.08
% 0.70/1.08 checksum: 2113284307
% 0.70/1.08
% 0.70/1.08
% 0.70/1.08 Bliksem ended
%------------------------------------------------------------------------------