TSTP Solution File: GEO237+3 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO237+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n015.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 02:53:09 EDT 2022
% Result : Theorem 0.46s 1.15s
% Output : Refutation 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO237+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.14 % Command : bliksem %s
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % DateTime : Sat Jun 18 14:06:43 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.46/1.15 *** allocated 10000 integers for termspace/termends
% 0.46/1.15 *** allocated 10000 integers for clauses
% 0.46/1.15 *** allocated 10000 integers for justifications
% 0.46/1.15 Bliksem 1.12
% 0.46/1.15
% 0.46/1.15
% 0.46/1.15 Automatic Strategy Selection
% 0.46/1.15
% 0.46/1.15
% 0.46/1.15 Clauses:
% 0.46/1.15
% 0.46/1.15 { ! unequally_directed_opposite_lines( X, Y ), unequally_directed_lines( X
% 0.46/1.15 , reverse_line( Y ) ) }.
% 0.46/1.15 { ! unequally_directed_lines( X, reverse_line( Y ) ),
% 0.46/1.15 unequally_directed_opposite_lines( X, Y ) }.
% 0.46/1.15 { ! right_apart_point( X, Y ), left_apart_point( X, reverse_line( Y ) ) }.
% 0.46/1.15 { ! left_apart_point( X, reverse_line( Y ) ), right_apart_point( X, Y ) }.
% 0.46/1.15 { ! right_convergent_lines( X, Y ), left_convergent_lines( X, reverse_line
% 0.46/1.15 ( Y ) ) }.
% 0.46/1.15 { ! left_convergent_lines( X, reverse_line( Y ) ), right_convergent_lines(
% 0.46/1.15 X, Y ) }.
% 0.46/1.15 { ! equally_directed_lines( X, Y ), ! unequally_directed_lines( X, Y ) }.
% 0.46/1.15 { unequally_directed_lines( X, Y ), equally_directed_lines( X, Y ) }.
% 0.46/1.15 { ! equally_directed_opposite_lines( X, Y ), !
% 0.46/1.15 unequally_directed_opposite_lines( X, Y ) }.
% 0.46/1.15 { unequally_directed_opposite_lines( X, Y ),
% 0.46/1.15 equally_directed_opposite_lines( X, Y ) }.
% 0.46/1.15 { ! apart_point_and_line( X, Y ), left_apart_point( X, Y ),
% 0.46/1.15 right_apart_point( X, Y ) }.
% 0.46/1.15 { ! left_apart_point( X, Y ), apart_point_and_line( X, Y ) }.
% 0.46/1.15 { ! right_apart_point( X, Y ), apart_point_and_line( X, Y ) }.
% 0.46/1.15 { ! convergent_lines( X, Y ), unequally_directed_lines( X, Y ) }.
% 0.46/1.15 { ! convergent_lines( X, Y ), unequally_directed_opposite_lines( X, Y ) }.
% 0.46/1.15 { ! unequally_directed_lines( X, Y ), ! unequally_directed_opposite_lines(
% 0.46/1.15 X, Y ), convergent_lines( X, Y ) }.
% 0.46/1.15 { ! divides_points( Z, X, Y ), alpha1( X, Y, Z ), alpha4( X, Y, Z ) }.
% 0.46/1.15 { ! alpha1( X, Y, Z ), divides_points( Z, X, Y ) }.
% 0.46/1.15 { ! alpha4( X, Y, Z ), divides_points( Z, X, Y ) }.
% 0.46/1.15 { ! alpha4( X, Y, Z ), right_apart_point( X, Z ) }.
% 0.46/1.15 { ! alpha4( X, Y, Z ), left_apart_point( Y, Z ) }.
% 0.46/1.15 { ! right_apart_point( X, Z ), ! left_apart_point( Y, Z ), alpha4( X, Y, Z
% 0.46/1.15 ) }.
% 0.46/1.15 { ! alpha1( X, Y, Z ), left_apart_point( X, Z ) }.
% 0.46/1.15 { ! alpha1( X, Y, Z ), right_apart_point( Y, Z ) }.
% 0.46/1.15 { ! left_apart_point( X, Z ), ! right_apart_point( Y, Z ), alpha1( X, Y, Z
% 0.46/1.15 ) }.
% 0.46/1.15 { ! before_on_line( X, Y, Z ), distinct_points( Y, Z ) }.
% 0.46/1.15 { ! before_on_line( X, Y, Z ), alpha2( X, Y, Z ) }.
% 0.46/1.15 { ! distinct_points( Y, Z ), ! alpha2( X, Y, Z ), before_on_line( X, Y, Z )
% 0.46/1.15 }.
% 0.46/1.15 { ! alpha2( X, Y, Z ), incident_point_and_line( Y, X ) }.
% 0.46/1.15 { ! alpha2( X, Y, Z ), alpha5( X, Y, Z ) }.
% 0.46/1.15 { ! incident_point_and_line( Y, X ), ! alpha5( X, Y, Z ), alpha2( X, Y, Z )
% 0.46/1.15 }.
% 0.46/1.15 { ! alpha5( X, Y, Z ), incident_point_and_line( Z, X ) }.
% 0.46/1.15 { ! alpha5( X, Y, Z ), equally_directed_lines( X, line_connecting( Y, Z ) )
% 0.46/1.15 }.
% 0.46/1.15 { ! incident_point_and_line( Z, X ), ! equally_directed_lines( X,
% 0.46/1.15 line_connecting( Y, Z ) ), alpha5( X, Y, Z ) }.
% 0.46/1.15 { ! between_on_line( X, Y, Z, T ), alpha3( X, Y, Z, T ), alpha6( X, Y, Z, T
% 0.46/1.15 ) }.
% 0.46/1.15 { ! alpha3( X, Y, Z, T ), between_on_line( X, Y, Z, T ) }.
% 0.46/1.15 { ! alpha6( X, Y, Z, T ), between_on_line( X, Y, Z, T ) }.
% 0.46/1.15 { ! alpha6( X, Y, Z, T ), before_on_line( X, T, Z ) }.
% 0.46/1.15 { ! alpha6( X, Y, Z, T ), before_on_line( X, Z, Y ) }.
% 0.46/1.15 { ! before_on_line( X, T, Z ), ! before_on_line( X, Z, Y ), alpha6( X, Y, Z
% 0.46/1.15 , T ) }.
% 0.46/1.15 { ! alpha3( X, Y, Z, T ), before_on_line( X, Y, Z ) }.
% 0.46/1.15 { ! alpha3( X, Y, Z, T ), before_on_line( X, Z, T ) }.
% 0.46/1.15 { ! before_on_line( X, Y, Z ), ! before_on_line( X, Z, T ), alpha3( X, Y, Z
% 0.46/1.15 , T ) }.
% 0.46/1.15 { ! distinct_points( X, X ) }.
% 0.46/1.15 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 0.46/1.15 ) }.
% 0.46/1.15 { ! distinct_lines( X, X ) }.
% 0.46/1.15 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.46/1.15 }.
% 0.46/1.15 { equally_directed_lines( X, X ) }.
% 0.46/1.15 { ! unequally_directed_lines( X, Y ), unequally_directed_lines( X, Z ),
% 0.46/1.15 unequally_directed_lines( Y, Z ) }.
% 0.46/1.15 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.46/1.15 reverse_line( Y ) ), alpha7( X, Z ), unequally_directed_lines( Y, Z ) }.
% 0.46/1.15 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.46/1.15 reverse_line( Y ) ), alpha7( X, Z ), unequally_directed_lines( Y,
% 0.46/1.15 reverse_line( Z ) ) }.
% 0.46/1.15 { ! alpha7( X, Y ), unequally_directed_lines( X, Y ) }.
% 0.46/1.15 { ! alpha7( X, Y ), unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.46/1.15 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.46/1.15 reverse_line( Y ) ), alpha7( X, Y ) }.
% 0.46/1.15 { unequally_directed_lines( X, Y ), unequally_directed_lines( X,
% 0.46/1.15 reverse_line( Y ) ) }.
% 0.46/1.15 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.46/1.15 reverse_line( Y ) ), left_convergent_lines( X, Y ), left_convergent_lines
% 0.46/1.15 ( X, reverse_line( Y ) ) }.
% 0.46/1.15 { ! left_apart_point( X, Y ) }.
% 0.46/1.15 { ! left_apart_point( X, reverse_line( Y ) ) }.
% 0.46/1.15 { ! left_convergent_lines( X, Y ) }.
% 0.46/1.15 { ! left_convergent_lines( X, reverse_line( Y ) ) }.
% 0.46/1.15 { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line(
% 0.46/1.15 line_connecting( X, Y ) ) }.
% 0.46/1.15 { ! line( X ), ! line( Y ), ! unequally_directed_lines( X, Y ), !
% 0.46/1.15 unequally_directed_lines( X, reverse_line( Y ) ), point(
% 0.46/1.15 intersection_point( X, Y ) ) }.
% 0.46/1.15 { ! point( Y ), ! line( X ), line( parallel_through_point( X, Y ) ) }.
% 0.46/1.15 { ! line( X ), line( reverse_line( X ) ) }.
% 0.46/1.15 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 0.46/1.15 , Y ) ) }.
% 0.46/1.15 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 0.46/1.15 , Y ) ) }.
% 0.46/1.15 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.46/1.15 reverse_line( Y ) ), ! apart_point_and_line( intersection_point( X, Y ),
% 0.46/1.15 X ) }.
% 0.46/1.15 { ! unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.46/1.15 reverse_line( Y ) ), ! apart_point_and_line( intersection_point( X, Y ),
% 0.46/1.15 Y ) }.
% 0.46/1.15 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 0.46/1.15 { ! distinct_lines( X, reverse_line( X ) ) }.
% 0.46/1.15 { ! distinct_points( X, Y ), equally_directed_lines( line_connecting( X, Y
% 0.46/1.15 ), reverse_line( line_connecting( Y, X ) ) ) }.
% 0.46/1.15 { equally_directed_lines( parallel_through_point( Y, X ), Y ) }.
% 0.46/1.15 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), left_apart_point( X
% 0.46/1.15 , Z ), left_apart_point( Y, Z ), left_apart_point( X, T ),
% 0.46/1.15 left_apart_point( Y, T ), left_apart_point( X, reverse_line( Z ) ),
% 0.46/1.15 left_apart_point( Y, reverse_line( Z ) ), left_apart_point( X,
% 0.46/1.15 reverse_line( T ) ), left_apart_point( Y, reverse_line( T ) ) }.
% 0.46/1.15 { ! distinct_points( X, Y ), ! left_apart_point( X, Z ), left_apart_point(
% 0.46/1.15 Y, Z ), left_convergent_lines( line_connecting( X, Y ), Z ) }.
% 0.46/1.15 { ! left_apart_point( X, Y ), distinct_points( X, Z ), left_apart_point( Z
% 0.46/1.15 , Y ) }.
% 0.46/1.15 { ! left_apart_point( X, Y ), ! unequally_directed_lines( Y, Z ),
% 0.46/1.15 distinct_lines( Y, Z ), left_apart_point( X, reverse_line( Z ) ) }.
% 0.46/1.15 { ! left_convergent_lines( X, Y ), unequally_directed_lines( Y, Z ),
% 0.46/1.15 left_convergent_lines( X, Z ) }.
% 0.46/1.15 { apart_point_and_line( skol1, skol2 ) }.
% 0.46/1.15 { divides_points( skol2, skol3, skol4 ) }.
% 0.46/1.15 { ! divides_points( skol2, skol3, skol1 ) }.
% 0.46/1.15 { ! divides_points( skol2, skol4, skol1 ) }.
% 0.46/1.15
% 0.46/1.15 percentage equality = 0.000000, percentage horn = 0.826667
% 0.46/1.15 This a non-horn, non-equality problem
% 0.46/1.15
% 0.46/1.15
% 0.46/1.15 Options Used:
% 0.46/1.15
% 0.46/1.15 useres = 1
% 0.46/1.15 useparamod = 0
% 0.46/1.15 useeqrefl = 0
% 0.46/1.15 useeqfact = 0
% 0.46/1.15 usefactor = 1
% 0.46/1.15 usesimpsplitting = 0
% 0.46/1.15 usesimpdemod = 0
% 0.46/1.15 usesimpres = 3
% 0.46/1.15
% 0.46/1.15 resimpinuse = 1000
% 0.46/1.15 resimpclauses = 20000
% 0.46/1.15 substype = standard
% 0.46/1.15 backwardsubs = 1
% 0.46/1.15 selectoldest = 5
% 0.46/1.15
% 0.46/1.15 litorderings [0] = split
% 0.46/1.15 litorderings [1] = liftord
% 0.46/1.15
% 0.46/1.15 termordering = none
% 0.46/1.15
% 0.46/1.15 litapriori = 1
% 0.46/1.15 termapriori = 0
% 0.46/1.15 litaposteriori = 0
% 0.46/1.15 termaposteriori = 0
% 0.46/1.15 demodaposteriori = 0
% 0.46/1.15 ordereqreflfact = 0
% 0.46/1.15
% 0.46/1.15 litselect = none
% 0.46/1.15
% 0.46/1.15 maxweight = 15
% 0.46/1.15 maxdepth = 30000
% 0.46/1.15 maxlength = 115
% 0.46/1.15 maxnrvars = 195
% 0.46/1.15 excuselevel = 1
% 0.46/1.15 increasemaxweight = 1
% 0.46/1.15
% 0.46/1.15 maxselected = 10000000
% 0.46/1.15 maxnrclauses = 10000000
% 0.46/1.15
% 0.46/1.15 showgenerated = 0
% 0.46/1.15 showkept = 0
% 0.46/1.15 showselected = 0
% 0.46/1.15 showdeleted = 0
% 0.46/1.15 showresimp = 1
% 0.46/1.15 showstatus = 2000
% 0.46/1.15
% 0.46/1.15 prologoutput = 0
% 0.46/1.15 nrgoals = 5000000
% 0.46/1.15 totalproof = 1
% 0.46/1.15
% 0.46/1.15 Symbols occurring in the translation:
% 0.46/1.15
% 0.46/1.15 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.46/1.15 . [1, 2] (w:1, o:26, a:1, s:1, b:0),
% 0.46/1.15 ! [4, 1] (w:0, o:18, a:1, s:1, b:0),
% 0.46/1.15 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.46/1.15 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.46/1.15 unequally_directed_opposite_lines [37, 2] (w:1, o:50, a:1, s:1, b:0)
% 0.46/1.15 ,
% 0.46/1.15 reverse_line [38, 1] (w:1, o:23, a:1, s:1, b:0),
% 0.46/1.15 unequally_directed_lines [39, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.46/1.15 right_apart_point [40, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.46/1.15 left_apart_point [41, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.46/1.15 right_convergent_lines [42, 2] (w:1, o:54, a:1, s:1, b:0),
% 0.46/1.15 left_convergent_lines [43, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.46/1.15 equally_directed_lines [44, 2] (w:1, o:58, a:1, s:1, b:0),
% 0.46/1.15 equally_directed_opposite_lines [45, 2] (w:1, o:59, a:1, s:1, b:0),
% 0.46/1.15 apart_point_and_line [48, 2] (w:1, o:60, a:1, s:1, b:0),
% 0.46/1.15 convergent_lines [50, 2] (w:1, o:61, a:1, s:1, b:0),
% 0.46/1.15 divides_points [52, 3] (w:1, o:67, a:1, s:1, b:0),
% 0.46/1.15 before_on_line [53, 3] (w:1, o:72, a:1, s:1, b:0),
% 0.46/1.15 distinct_points [54, 2] (w:1, o:56, a:1, s:1, b:0),
% 0.46/1.15 incident_point_and_line [55, 2] (w:1, o:62, a:1, s:1, b:0),
% 0.46/1.15 line_connecting [56, 2] (w:1, o:63, a:1, s:1, b:0),
% 0.46/1.15 between_on_line [58, 4] (w:1, o:75, a:1, s:1, b:0),
% 0.46/1.15 distinct_lines [59, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.46/1.15 point [61, 1] (w:1, o:24, a:1, s:1, b:0),
% 0.46/1.15 line [62, 1] (w:1, o:25, a:1, s:1, b:0),
% 0.46/1.15 intersection_point [63, 2] (w:1, o:64, a:1, s:1, b:0),
% 0.46/1.15 parallel_through_point [64, 2] (w:1, o:65, a:1, s:1, b:0),
% 0.46/1.15 alpha1 [65, 3] (w:1, o:68, a:1, s:1, b:0),
% 0.46/1.15 alpha2 [66, 3] (w:1, o:69, a:1, s:1, b:0),
% 0.46/1.15 alpha3 [67, 4] (w:1, o:73, a:1, s:1, b:0),
% 0.46/1.15 alpha4 [68, 3] (w:1, o:70, a:1, s:1, b:0),
% 0.46/1.15 alpha5 [69, 3] (w:1, o:71, a:1, s:1, b:0),
% 0.46/1.15 alpha6 [70, 4] (w:1, o:74, a:1, s:1, b:0),
% 0.46/1.15 alpha7 [71, 2] (w:1, o:66, a:1, s:1, b:0),
% 0.46/1.15 skol1 [72, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.46/1.15 skol2 [73, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.46/1.15 skol3 [74, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.46/1.15 skol4 [75, 0] (w:1, o:17, a:1, s:1, b:0).
% 0.46/1.15
% 0.46/1.15
% 0.46/1.15 Starting Search:
% 0.46/1.15
% 0.46/1.15
% 0.46/1.15 Bliksems!, er is een bewijs:
% 0.46/1.15 % SZS status Theorem
% 0.46/1.15 % SZS output start Refutation
% 0.46/1.15
% 0.46/1.15 (2) {G0,W7,D3,L2,V2,M1} I { ! right_apart_point( X, Y ), left_apart_point(
% 0.46/1.15 X, reverse_line( Y ) ) }.
% 0.46/1.15 (10) {G0,W9,D2,L3,V2,M1} I { left_apart_point( X, Y ), right_apart_point( X
% 0.46/1.15 , Y ), ! apart_point_and_line( X, Y ) }.
% 0.46/1.15 (56) {G0,W3,D2,L1,V2,M1} I { ! left_apart_point( X, Y ) }.
% 0.46/1.15 (71) {G0,W3,D2,L1,V0,M1} I { apart_point_and_line( skol1, skol2 ) }.
% 0.46/1.15 (80) {G1,W3,D2,L1,V2,M1} S(2);r(56) { ! right_apart_point( X, Y ) }.
% 0.46/1.15 (89) {G2,W3,D2,L1,V2,M1} S(10);r(56);r(80) { ! apart_point_and_line( X, Y )
% 0.46/1.15 }.
% 0.46/1.15 (90) {G3,W0,D0,L0,V0,M0} R(89,71) { }.
% 0.46/1.15
% 0.46/1.15
% 0.46/1.15 % SZS output end Refutation
% 0.46/1.15 found a proof!
% 0.46/1.15
% 0.46/1.15
% 0.46/1.15 Unprocessed initial clauses:
% 0.46/1.15
% 0.46/1.15 (92) {G0,W7,D3,L2,V2,M2} { ! unequally_directed_opposite_lines( X, Y ),
% 0.46/1.15 unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.46/1.15 (93) {G0,W7,D3,L2,V2,M2} { ! unequally_directed_lines( X, reverse_line( Y
% 0.46/1.15 ) ), unequally_directed_opposite_lines( X, Y ) }.
% 0.46/1.15 (94) {G0,W7,D3,L2,V2,M2} { ! right_apart_point( X, Y ), left_apart_point(
% 0.46/1.15 X, reverse_line( Y ) ) }.
% 0.46/1.15 (95) {G0,W7,D3,L2,V2,M2} { ! left_apart_point( X, reverse_line( Y ) ),
% 0.46/1.15 right_apart_point( X, Y ) }.
% 0.46/1.15 (96) {G0,W7,D3,L2,V2,M2} { ! right_convergent_lines( X, Y ),
% 0.46/1.15 left_convergent_lines( X, reverse_line( Y ) ) }.
% 0.46/1.15 (97) {G0,W7,D3,L2,V2,M2} { ! left_convergent_lines( X, reverse_line( Y ) )
% 0.46/1.15 , right_convergent_lines( X, Y ) }.
% 0.46/1.15 (98) {G0,W6,D2,L2,V2,M2} { ! equally_directed_lines( X, Y ), !
% 0.46/1.15 unequally_directed_lines( X, Y ) }.
% 0.46/1.15 (99) {G0,W6,D2,L2,V2,M2} { unequally_directed_lines( X, Y ),
% 0.46/1.15 equally_directed_lines( X, Y ) }.
% 0.46/1.15 (100) {G0,W6,D2,L2,V2,M2} { ! equally_directed_opposite_lines( X, Y ), !
% 0.46/1.15 unequally_directed_opposite_lines( X, Y ) }.
% 0.46/1.15 (101) {G0,W6,D2,L2,V2,M2} { unequally_directed_opposite_lines( X, Y ),
% 0.46/1.15 equally_directed_opposite_lines( X, Y ) }.
% 0.46/1.15 (102) {G0,W9,D2,L3,V2,M3} { ! apart_point_and_line( X, Y ),
% 0.46/1.15 left_apart_point( X, Y ), right_apart_point( X, Y ) }.
% 0.46/1.15 (103) {G0,W6,D2,L2,V2,M2} { ! left_apart_point( X, Y ),
% 0.46/1.15 apart_point_and_line( X, Y ) }.
% 0.46/1.15 (104) {G0,W6,D2,L2,V2,M2} { ! right_apart_point( X, Y ),
% 0.46/1.15 apart_point_and_line( X, Y ) }.
% 0.46/1.15 (105) {G0,W6,D2,L2,V2,M2} { ! convergent_lines( X, Y ),
% 0.46/1.15 unequally_directed_lines( X, Y ) }.
% 0.46/1.15 (106) {G0,W6,D2,L2,V2,M2} { ! convergent_lines( X, Y ),
% 0.46/1.15 unequally_directed_opposite_lines( X, Y ) }.
% 0.46/1.15 (107) {G0,W9,D2,L3,V2,M3} { ! unequally_directed_lines( X, Y ), !
% 0.46/1.15 unequally_directed_opposite_lines( X, Y ), convergent_lines( X, Y ) }.
% 0.46/1.15 (108) {G0,W12,D2,L3,V3,M3} { ! divides_points( Z, X, Y ), alpha1( X, Y, Z
% 0.46/1.15 ), alpha4( X, Y, Z ) }.
% 0.46/1.15 (109) {G0,W8,D2,L2,V3,M2} { ! alpha1( X, Y, Z ), divides_points( Z, X, Y )
% 0.46/1.15 }.
% 0.46/1.15 (110) {G0,W8,D2,L2,V3,M2} { ! alpha4( X, Y, Z ), divides_points( Z, X, Y )
% 0.46/1.15 }.
% 0.46/1.15 (111) {G0,W7,D2,L2,V3,M2} { ! alpha4( X, Y, Z ), right_apart_point( X, Z )
% 0.46/1.15 }.
% 0.46/1.15 (112) {G0,W7,D2,L2,V3,M2} { ! alpha4( X, Y, Z ), left_apart_point( Y, Z )
% 0.46/1.15 }.
% 0.46/1.15 (113) {G0,W10,D2,L3,V3,M3} { ! right_apart_point( X, Z ), !
% 0.46/1.15 left_apart_point( Y, Z ), alpha4( X, Y, Z ) }.
% 0.46/1.15 (114) {G0,W7,D2,L2,V3,M2} { ! alpha1( X, Y, Z ), left_apart_point( X, Z )
% 0.46/1.15 }.
% 0.46/1.15 (115) {G0,W7,D2,L2,V3,M2} { ! alpha1( X, Y, Z ), right_apart_point( Y, Z )
% 0.46/1.15 }.
% 0.46/1.15 (116) {G0,W10,D2,L3,V3,M3} { ! left_apart_point( X, Z ), !
% 0.46/1.15 right_apart_point( Y, Z ), alpha1( X, Y, Z ) }.
% 0.46/1.15 (117) {G0,W7,D2,L2,V3,M2} { ! before_on_line( X, Y, Z ), distinct_points(
% 0.46/1.15 Y, Z ) }.
% 0.46/1.15 (118) {G0,W8,D2,L2,V3,M2} { ! before_on_line( X, Y, Z ), alpha2( X, Y, Z )
% 0.46/1.15 }.
% 0.46/1.15 (119) {G0,W11,D2,L3,V3,M3} { ! distinct_points( Y, Z ), ! alpha2( X, Y, Z
% 0.46/1.15 ), before_on_line( X, Y, Z ) }.
% 0.46/1.15 (120) {G0,W7,D2,L2,V3,M2} { ! alpha2( X, Y, Z ), incident_point_and_line(
% 0.46/1.15 Y, X ) }.
% 0.46/1.15 (121) {G0,W8,D2,L2,V3,M2} { ! alpha2( X, Y, Z ), alpha5( X, Y, Z ) }.
% 0.46/1.15 (122) {G0,W11,D2,L3,V3,M3} { ! incident_point_and_line( Y, X ), ! alpha5(
% 0.46/1.15 X, Y, Z ), alpha2( X, Y, Z ) }.
% 0.46/1.15 (123) {G0,W7,D2,L2,V3,M2} { ! alpha5( X, Y, Z ), incident_point_and_line(
% 0.46/1.15 Z, X ) }.
% 0.46/1.15 (124) {G0,W9,D3,L2,V3,M2} { ! alpha5( X, Y, Z ), equally_directed_lines( X
% 0.46/1.15 , line_connecting( Y, Z ) ) }.
% 0.46/1.15 (125) {G0,W12,D3,L3,V3,M3} { ! incident_point_and_line( Z, X ), !
% 0.46/1.15 equally_directed_lines( X, line_connecting( Y, Z ) ), alpha5( X, Y, Z )
% 0.46/1.15 }.
% 0.46/1.15 (126) {G0,W15,D2,L3,V4,M3} { ! between_on_line( X, Y, Z, T ), alpha3( X, Y
% 0.46/1.15 , Z, T ), alpha6( X, Y, Z, T ) }.
% 0.46/1.15 (127) {G0,W10,D2,L2,V4,M2} { ! alpha3( X, Y, Z, T ), between_on_line( X, Y
% 0.46/1.15 , Z, T ) }.
% 0.46/1.15 (128) {G0,W10,D2,L2,V4,M2} { ! alpha6( X, Y, Z, T ), between_on_line( X, Y
% 0.46/1.15 , Z, T ) }.
% 0.46/1.15 (129) {G0,W9,D2,L2,V4,M2} { ! alpha6( X, Y, Z, T ), before_on_line( X, T,
% 0.46/1.15 Z ) }.
% 0.46/1.15 (130) {G0,W9,D2,L2,V4,M2} { ! alpha6( X, Y, Z, T ), before_on_line( X, Z,
% 0.46/1.15 Y ) }.
% 0.46/1.15 (131) {G0,W13,D2,L3,V4,M3} { ! before_on_line( X, T, Z ), ! before_on_line
% 0.46/1.15 ( X, Z, Y ), alpha6( X, Y, Z, T ) }.
% 0.46/1.15 (132) {G0,W9,D2,L2,V4,M2} { ! alpha3( X, Y, Z, T ), before_on_line( X, Y,
% 0.46/1.15 Z ) }.
% 0.46/1.15 (133) {G0,W9,D2,L2,V4,M2} { ! alpha3( X, Y, Z, T ), before_on_line( X, Z,
% 0.46/1.15 T ) }.
% 0.46/1.15 (134) {G0,W13,D2,L3,V4,M3} { ! before_on_line( X, Y, Z ), ! before_on_line
% 0.46/1.15 ( X, Z, T ), alpha3( X, Y, Z, T ) }.
% 0.46/1.15 (135) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 0.46/1.15 (136) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 0.46/1.15 , Z ), distinct_points( Y, Z ) }.
% 0.46/1.15 (137) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.46/1.15 (138) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X, Z
% 0.46/1.15 ), distinct_lines( Y, Z ) }.
% 0.46/1.15 (139) {G0,W3,D2,L1,V1,M1} { equally_directed_lines( X, X ) }.
% 0.46/1.15 (140) {G0,W9,D2,L3,V3,M3} { ! unequally_directed_lines( X, Y ),
% 0.46/1.15 unequally_directed_lines( X, Z ), unequally_directed_lines( Y, Z ) }.
% 0.46/1.15 (141) {G0,W13,D3,L4,V3,M4} { ! unequally_directed_lines( X, Y ), !
% 0.46/1.15 unequally_directed_lines( X, reverse_line( Y ) ), alpha7( X, Z ),
% 0.46/1.15 unequally_directed_lines( Y, Z ) }.
% 0.46/1.15 (142) {G0,W14,D3,L4,V3,M4} { ! unequally_directed_lines( X, Y ), !
% 0.46/1.15 unequally_directed_lines( X, reverse_line( Y ) ), alpha7( X, Z ),
% 0.46/1.15 unequally_directed_lines( Y, reverse_line( Z ) ) }.
% 0.46/1.15 (143) {G0,W6,D2,L2,V2,M2} { ! alpha7( X, Y ), unequally_directed_lines( X
% 0.46/1.15 , Y ) }.
% 0.46/1.15 (144) {G0,W7,D3,L2,V2,M2} { ! alpha7( X, Y ), unequally_directed_lines( X
% 0.46/1.15 , reverse_line( Y ) ) }.
% 0.46/1.15 (145) {G0,W10,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y ), !
% 0.46/1.15 unequally_directed_lines( X, reverse_line( Y ) ), alpha7( X, Y ) }.
% 0.46/1.15 (146) {G0,W7,D3,L2,V2,M2} { unequally_directed_lines( X, Y ),
% 0.46/1.15 unequally_directed_lines( X, reverse_line( Y ) ) }.
% 0.46/1.15 (147) {G0,W14,D3,L4,V2,M4} { ! unequally_directed_lines( X, Y ), !
% 0.46/1.15 unequally_directed_lines( X, reverse_line( Y ) ), left_convergent_lines(
% 0.46/1.15 X, Y ), left_convergent_lines( X, reverse_line( Y ) ) }.
% 0.46/1.15 (148) {G0,W3,D2,L1,V2,M1} { ! left_apart_point( X, Y ) }.
% 0.46/1.15 (149) {G0,W4,D3,L1,V2,M1} { ! left_apart_point( X, reverse_line( Y ) ) }.
% 0.46/1.15 (150) {G0,W3,D2,L1,V2,M1} { ! left_convergent_lines( X, Y ) }.
% 0.46/1.15 (151) {G0,W4,D3,L1,V2,M1} { ! left_convergent_lines( X, reverse_line( Y )
% 0.46/1.15 ) }.
% 0.46/1.15 (152) {G0,W11,D3,L4,V2,M4} { ! point( X ), ! point( Y ), ! distinct_points
% 0.46/1.15 ( X, Y ), line( line_connecting( X, Y ) ) }.
% 0.46/1.15 (153) {G0,W15,D3,L5,V2,M5} { ! line( X ), ! line( Y ), !
% 0.46/1.15 unequally_directed_lines( X, Y ), ! unequally_directed_lines( X,
% 0.46/1.15 reverse_line( Y ) ), point( intersection_point( X, Y ) ) }.
% 0.46/1.15 (154) {G0,W8,D3,L3,V2,M3} { ! point( Y ), ! line( X ), line(
% 0.46/1.15 parallel_through_point( X, Y ) ) }.
% 0.46/1.15 (155) {G0,W5,D3,L2,V1,M2} { ! line( X ), line( reverse_line( X ) ) }.
% 0.46/1.15 (156) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.46/1.15 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 0.46/1.15 (157) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.46/1.15 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 0.46/1.15 (158) {G0,W12,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y ), !
% 0.46/1.15 unequally_directed_lines( X, reverse_line( Y ) ), ! apart_point_and_line
% 0.46/1.15 ( intersection_point( X, Y ), X ) }.
% 0.46/1.15 (159) {G0,W12,D3,L3,V2,M3} { ! unequally_directed_lines( X, Y ), !
% 0.46/1.15 unequally_directed_lines( X, reverse_line( Y ) ), ! apart_point_and_line
% 0.46/1.15 ( intersection_point( X, Y ), Y ) }.
% 0.46/1.15 (160) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.46/1.15 parallel_through_point( Y, X ) ) }.
% 0.46/1.15 (161) {G0,W4,D3,L1,V1,M1} { ! distinct_lines( X, reverse_line( X ) ) }.
% 0.46/1.15 (162) {G0,W11,D4,L2,V2,M2} { ! distinct_points( X, Y ),
% 0.46/1.15 equally_directed_lines( line_connecting( X, Y ), reverse_line(
% 0.46/1.15 line_connecting( Y, X ) ) ) }.
% 0.46/1.15 (163) {G0,W5,D3,L1,V2,M1} { equally_directed_lines( parallel_through_point
% 0.46/1.15 ( Y, X ), Y ) }.
% 0.46/1.15 (164) {G0,W34,D3,L10,V4,M10} { ! distinct_points( X, Y ), ! distinct_lines
% 0.46/1.15 ( Z, T ), left_apart_point( X, Z ), left_apart_point( Y, Z ),
% 0.46/1.15 left_apart_point( X, T ), left_apart_point( Y, T ), left_apart_point( X,
% 0.46/1.15 reverse_line( Z ) ), left_apart_point( Y, reverse_line( Z ) ),
% 0.46/1.15 left_apart_point( X, reverse_line( T ) ), left_apart_point( Y,
% 0.46/1.15 reverse_line( T ) ) }.
% 0.46/1.15 (165) {G0,W14,D3,L4,V3,M4} { ! distinct_points( X, Y ), ! left_apart_point
% 0.46/1.15 ( X, Z ), left_apart_point( Y, Z ), left_convergent_lines(
% 0.46/1.15 line_connecting( X, Y ), Z ) }.
% 0.46/1.15 (166) {G0,W9,D2,L3,V3,M3} { ! left_apart_point( X, Y ), distinct_points( X
% 0.46/1.15 , Z ), left_apart_point( Z, Y ) }.
% 0.46/1.15 (167) {G0,W13,D3,L4,V3,M4} { ! left_apart_point( X, Y ), !
% 0.46/1.15 unequally_directed_lines( Y, Z ), distinct_lines( Y, Z ),
% 0.46/1.15 left_apart_point( X, reverse_line( Z ) ) }.
% 0.46/1.15 (168) {G0,W9,D2,L3,V3,M3} { ! left_convergent_lines( X, Y ),
% 0.46/1.15 unequally_directed_lines( Y, Z ), left_convergent_lines( X, Z ) }.
% 0.46/1.15 (169) {G0,W3,D2,L1,V0,M1} { apart_point_and_line( skol1, skol2 ) }.
% 0.46/1.15 (170) {G0,W4,D2,L1,V0,M1} { divides_points( skol2, skol3, skol4 ) }.
% 0.46/1.15 (171) {G0,W4,D2,L1,V0,M1} { ! divides_points( skol2, skol3, skol1 ) }.
% 0.46/1.15 (172) {G0,W4,D2,L1,V0,M1} { ! divides_points( skol2, skol4, skol1 ) }.
% 0.46/1.15
% 0.46/1.15
% 0.46/1.15 Total Proof:
% 0.46/1.15
% 0.46/1.15 subsumption: (2) {G0,W7,D3,L2,V2,M1} I { ! right_apart_point( X, Y ),
% 0.46/1.15 left_apart_point( X, reverse_line( Y ) ) }.
% 0.46/1.15 parent0: (94) {G0,W7,D3,L2,V2,M2} { ! right_apart_point( X, Y ),
% 0.46/1.15 left_apart_point( X, reverse_line( Y ) ) }.
% 0.46/1.15 substitution0:
% 0.46/1.15 X := X
% 0.46/1.15 Y := Y
% 0.46/1.15 end
% 0.46/1.15 permutation0:
% 0.46/1.15 0 ==> 0
% 0.46/1.15 1 ==> 1
% 0.46/1.15 end
% 0.46/1.15
% 0.46/1.15 subsumption: (10) {G0,W9,D2,L3,V2,M1} I { left_apart_point( X, Y ),
% 0.46/1.15 right_apart_point( X, Y ), ! apart_point_and_line( X, Y ) }.
% 0.46/1.15 parent0: (102) {G0,W9,D2,L3,V2,M3} { ! apart_point_and_line( X, Y ),
% 0.46/1.15 left_apart_point( X, Y ), right_apart_point( X, Y ) }.
% 0.46/1.15 substitution0:
% 0.46/1.15 X := X
% 0.46/1.15 Y := Y
% 0.46/1.15 end
% 0.46/1.15 permutation0:
% 0.46/1.15 0 ==> 2
% 0.46/1.15 1 ==> 0
% 0.46/1.15 2 ==> 1
% 0.46/1.15 end
% 0.46/1.15
% 0.46/1.15 subsumption: (56) {G0,W3,D2,L1,V2,M1} I { ! left_apart_point( X, Y ) }.
% 0.46/1.15 parent0: (148) {G0,W3,D2,L1,V2,M1} { ! left_apart_point( X, Y ) }.
% 0.46/1.15 substitution0:
% 0.46/1.15 X := X
% 0.46/1.15 Y := Y
% 0.46/1.15 end
% 0.46/1.15 permutation0:
% 0.46/1.15 0 ==> 0
% 0.46/1.15 end
% 0.46/1.15
% 0.46/1.15 subsumption: (71) {G0,W3,D2,L1,V0,M1} I { apart_point_and_line( skol1,
% 0.46/1.15 skol2 ) }.
% 0.46/1.15 parent0: (169) {G0,W3,D2,L1,V0,M1} { apart_point_and_line( skol1, skol2 )
% 0.46/1.15 }.
% 0.46/1.15 substitution0:
% 0.46/1.15 end
% 0.46/1.15 permutation0:
% 0.46/1.15 0 ==> 0
% 0.46/1.15 end
% 0.46/1.15
% 0.46/1.15 resolution: (211) {G1,W3,D2,L1,V2,M1} { ! right_apart_point( X, Y ) }.
% 0.46/1.15 parent0[0]: (56) {G0,W3,D2,L1,V2,M1} I { ! left_apart_point( X, Y ) }.
% 0.46/1.15 parent1[1]: (2) {G0,W7,D3,L2,V2,M1} I { ! right_apart_point( X, Y ),
% 0.46/1.15 left_apart_point( X, reverse_line( Y ) ) }.
% 0.46/1.15 substitution0:
% 0.46/1.15 X := X
% 0.46/1.15 Y := reverse_line( Y )
% 0.46/1.15 end
% 0.46/1.15 substitution1:
% 0.46/1.15 X := X
% 0.46/1.15 Y := Y
% 0.46/1.15 end
% 0.46/1.15
% 0.46/1.15 subsumption: (80) {G1,W3,D2,L1,V2,M1} S(2);r(56) { ! right_apart_point( X,
% 0.46/1.15 Y ) }.
% 0.46/1.15 parent0: (211) {G1,W3,D2,L1,V2,M1} { ! right_apart_point( X, Y ) }.
% 0.46/1.15 substitution0:
% 0.46/1.15 X := X
% 0.46/1.15 Y := Y
% 0.46/1.15 end
% 0.46/1.15 permutation0:
% 0.46/1.15 0 ==> 0
% 0.46/1.15 end
% 0.46/1.15
% 0.46/1.15 resolution: (212) {G1,W6,D2,L2,V2,M2} { right_apart_point( X, Y ), !
% 0.46/1.15 apart_point_and_line( X, Y ) }.
% 0.46/1.15 parent0[0]: (56) {G0,W3,D2,L1,V2,M1} I { ! left_apart_point( X, Y ) }.
% 0.46/1.15 parent1[0]: (10) {G0,W9,D2,L3,V2,M1} I { left_apart_point( X, Y ),
% 0.46/1.15 right_apart_point( X, Y ), ! apart_point_and_line( X, Y ) }.
% 0.46/1.15 substitution0:
% 0.46/1.15 X := X
% 0.46/1.15 Y := Y
% 0.46/1.15 end
% 0.46/1.15 substitution1:
% 0.46/1.15 X := X
% 0.46/1.15 Y := Y
% 0.46/1.15 end
% 0.46/1.15
% 0.46/1.15 resolution: (213) {G2,W3,D2,L1,V2,M1} { ! apart_point_and_line( X, Y ) }.
% 0.46/1.15 parent0[0]: (80) {G1,W3,D2,L1,V2,M1} S(2);r(56) { ! right_apart_point( X, Y
% 0.46/1.15 ) }.
% 0.46/1.15 parent1[0]: (212) {G1,W6,D2,L2,V2,M2} { right_apart_point( X, Y ), !
% 0.46/1.15 apart_point_and_line( X, Y ) }.
% 0.46/1.15 substitution0:
% 0.46/1.15 X := X
% 0.46/1.15 Y := Y
% 0.46/1.15 end
% 0.46/1.15 substitution1:
% 0.46/1.15 X := X
% 0.46/1.15 Y := Y
% 0.46/1.15 end
% 0.46/1.15
% 0.46/1.15 subsumption: (89) {G2,W3,D2,L1,V2,M1} S(10);r(56);r(80) { !
% 0.46/1.15 apart_point_and_line( X, Y ) }.
% 0.46/1.15 parent0: (213) {G2,W3,D2,L1,V2,M1} { ! apart_point_and_line( X, Y ) }.
% 0.46/1.15 substitution0:
% 0.46/1.15 X := X
% 0.46/1.15 Y := Y
% 0.46/1.15 end
% 0.46/1.15 permutation0:
% 0.46/1.15 0 ==> 0
% 0.46/1.15 end
% 0.46/1.15
% 0.46/1.15 resolution: (214) {G1,W0,D0,L0,V0,M0} { }.
% 0.46/1.15 parent0[0]: (89) {G2,W3,D2,L1,V2,M1} S(10);r(56);r(80) { !
% 0.46/1.15 apart_point_and_line( X, Y ) }.
% 0.46/1.15 parent1[0]: (71) {G0,W3,D2,L1,V0,M1} I { apart_point_and_line( skol1, skol2
% 0.46/1.15 ) }.
% 0.46/1.15 substitution0:
% 0.46/1.15 X := skol1
% 0.46/1.15 Y := skol2
% 0.46/1.15 end
% 0.46/1.15 substitution1:
% 0.46/1.15 end
% 0.46/1.15
% 0.46/1.15 subsumption: (90) {G3,W0,D0,L0,V0,M0} R(89,71) { }.
% 0.46/1.15 parent0: (214) {G1,W0,D0,L0,V0,M0} { }.
% 0.46/1.15 substitution0:
% 0.46/1.15 end
% 0.46/1.15 permutation0:
% 0.46/1.15 end
% 0.46/1.15
% 0.46/1.15 Proof check complete!
% 0.46/1.15
% 0.46/1.15 Memory use:
% 0.46/1.15
% 0.46/1.15 space for terms: 2531
% 0.46/1.15 space for clauses: 5318
% 0.46/1.15
% 0.46/1.15
% 0.46/1.15 clauses generated: 124
% 0.46/1.15 clauses kept: 91
% 0.46/1.15 clauses selected: 30
% 0.46/1.15 clauses deleted: 7
% 0.46/1.15 clauses inuse deleted: 0
% 0.46/1.15
% 0.46/1.15 subsentry: 315
% 0.46/1.15 literals s-matched: 221
% 0.46/1.15 literals matched: 171
% 0.46/1.15 full subsumption: 60
% 0.46/1.15
% 0.46/1.15 checksum: 49981988
% 0.46/1.15
% 0.46/1.15
% 0.46/1.15 Bliksem ended
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