TSTP Solution File: GEO218+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO218+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n026.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 02:52:54 EDT 2022
% Result : Theorem 1.12s 1.48s
% Output : Refutation 1.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GEO218+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Sat Jun 18 18:38:09 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.12/1.48 *** allocated 10000 integers for termspace/termends
% 1.12/1.48 *** allocated 10000 integers for clauses
% 1.12/1.48 *** allocated 10000 integers for justifications
% 1.12/1.48 Bliksem 1.12
% 1.12/1.48
% 1.12/1.48
% 1.12/1.48 Automatic Strategy Selection
% 1.12/1.48
% 1.12/1.48
% 1.12/1.48 Clauses:
% 1.12/1.48
% 1.12/1.48 { ! distinct_points( X, X ) }.
% 1.12/1.48 { ! distinct_lines( X, X ) }.
% 1.12/1.48 { ! convergent_lines( X, X ) }.
% 1.12/1.48 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 1.12/1.48 ) }.
% 1.12/1.48 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 1.12/1.48 }.
% 1.12/1.48 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 1.12/1.48 , Z ) }.
% 1.12/1.48 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 1.12/1.48 , Y ) ) }.
% 1.12/1.48 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 1.12/1.48 , Y ) ) }.
% 1.12/1.48 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 1.12/1.48 , Y ), X ) }.
% 1.12/1.48 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 1.12/1.48 , Y ), Y ) }.
% 1.12/1.48 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 1.12/1.48 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 1.12/1.48 apart_point_and_line( Y, T ) }.
% 1.12/1.48 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 1.12/1.48 apart_point_and_line( Z, Y ) }.
% 1.12/1.48 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 1.12/1.48 apart_point_and_line( X, Z ) }.
% 1.12/1.48 { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X,
% 1.12/1.48 Z ) }.
% 1.12/1.48 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 1.12/1.48 { alpha1( X, Z ), convergent_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 1.12/1.48 unorthogonal_lines( X, Y ) }.
% 1.12/1.48 { alpha1( X, Z ), unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 1.12/1.48 unorthogonal_lines( X, Y ) }.
% 1.12/1.48 { ! alpha1( X, Y ), convergent_lines( Y, X ) }.
% 1.12/1.48 { ! alpha1( X, Y ), unorthogonal_lines( Y, X ) }.
% 1.12/1.48 { ! convergent_lines( Y, X ), ! unorthogonal_lines( Y, X ), alpha1( X, Y )
% 1.12/1.48 }.
% 1.12/1.48 { unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ), !
% 1.12/1.48 convergent_lines( X, Y ) }.
% 1.12/1.48 { ! convergent_lines( skol3, skol1 ) }.
% 1.12/1.48 { ! unorthogonal_lines( skol3, skol2 ) }.
% 1.12/1.48 { unorthogonal_lines( skol1, skol2 ) }.
% 1.12/1.48
% 1.12/1.48 percentage equality = 0.000000, percentage horn = 0.541667
% 1.12/1.48 This a non-horn, non-equality problem
% 1.12/1.48
% 1.12/1.48
% 1.12/1.48 Options Used:
% 1.12/1.48
% 1.12/1.48 useres = 1
% 1.12/1.48 useparamod = 0
% 1.12/1.48 useeqrefl = 0
% 1.12/1.48 useeqfact = 0
% 1.12/1.48 usefactor = 1
% 1.12/1.48 usesimpsplitting = 0
% 1.12/1.48 usesimpdemod = 0
% 1.12/1.48 usesimpres = 3
% 1.12/1.48
% 1.12/1.48 resimpinuse = 1000
% 1.12/1.48 resimpclauses = 20000
% 1.12/1.48 substype = standard
% 1.12/1.48 backwardsubs = 1
% 1.12/1.48 selectoldest = 5
% 1.12/1.48
% 1.12/1.48 litorderings [0] = split
% 1.12/1.48 litorderings [1] = liftord
% 1.12/1.48
% 1.12/1.48 termordering = none
% 1.12/1.48
% 1.12/1.48 litapriori = 1
% 1.12/1.48 termapriori = 0
% 1.12/1.48 litaposteriori = 0
% 1.12/1.48 termaposteriori = 0
% 1.12/1.48 demodaposteriori = 0
% 1.12/1.48 ordereqreflfact = 0
% 1.12/1.48
% 1.12/1.48 litselect = none
% 1.12/1.48
% 1.12/1.48 maxweight = 15
% 1.12/1.48 maxdepth = 30000
% 1.12/1.48 maxlength = 115
% 1.12/1.48 maxnrvars = 195
% 1.12/1.48 excuselevel = 1
% 1.12/1.48 increasemaxweight = 1
% 1.12/1.48
% 1.12/1.48 maxselected = 10000000
% 1.12/1.48 maxnrclauses = 10000000
% 1.12/1.48
% 1.12/1.48 showgenerated = 0
% 1.12/1.48 showkept = 0
% 1.12/1.48 showselected = 0
% 1.12/1.48 showdeleted = 0
% 1.12/1.48 showresimp = 1
% 1.12/1.48 showstatus = 2000
% 1.12/1.48
% 1.12/1.48 prologoutput = 0
% 1.12/1.48 nrgoals = 5000000
% 1.12/1.48 totalproof = 1
% 1.12/1.48
% 1.12/1.48 Symbols occurring in the translation:
% 1.12/1.48
% 1.12/1.48 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.12/1.48 . [1, 2] (w:1, o:22, a:1, s:1, b:0),
% 1.12/1.48 ! [4, 1] (w:0, o:17, a:1, s:1, b:0),
% 1.12/1.48 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.12/1.48 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.12/1.48 distinct_points [36, 2] (w:1, o:47, a:1, s:1, b:0),
% 1.12/1.48 distinct_lines [37, 2] (w:1, o:48, a:1, s:1, b:0),
% 1.12/1.48 convergent_lines [38, 2] (w:1, o:46, a:1, s:1, b:0),
% 1.12/1.48 line_connecting [41, 2] (w:1, o:49, a:1, s:1, b:0),
% 1.12/1.48 apart_point_and_line [42, 2] (w:1, o:50, a:1, s:1, b:0),
% 1.12/1.48 intersection_point [43, 2] (w:1, o:51, a:1, s:1, b:0),
% 1.12/1.48 unorthogonal_lines [48, 2] (w:1, o:52, a:1, s:1, b:0),
% 1.12/1.48 alpha1 [50, 2] (w:1, o:53, a:1, s:1, b:0),
% 1.12/1.48 skol1 [51, 0] (w:1, o:14, a:1, s:1, b:0),
% 1.12/1.48 skol2 [52, 0] (w:1, o:15, a:1, s:1, b:0),
% 1.12/1.48 skol3 [53, 0] (w:1, o:16, a:1, s:1, b:0).
% 1.12/1.48
% 1.12/1.48
% 1.12/1.48 Starting Search:
% 1.12/1.48
% 1.12/1.48 *** allocated 15000 integers for clauses
% 1.12/1.48 *** allocated 22500 integers for clauses
% 1.12/1.48 *** allocated 33750 integers for clauses
% 1.12/1.48
% 1.12/1.48 Bliksems!, er is een bewijs:
% 1.12/1.48 % SZS status Theorem
% 1.12/1.48 % SZS output start Refutation
% 1.12/1.48
% 1.12/1.48 (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 1.12/1.48 (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), convergent_lines( Y,
% 1.12/1.48 Z ), ! convergent_lines( X, Y ) }.
% 1.12/1.48 (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), unorthogonal_lines(
% 1.12/1.48 X, Y ) }.
% 1.12/1.48 (15) {G0,W12,D2,L4,V3,M1} I { convergent_lines( Z, Y ), ! convergent_lines
% 1.12/1.48 ( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z ) }.
% 1.12/1.48 (18) {G0,W6,D2,L2,V2,M1} I { unorthogonal_lines( Y, X ), ! alpha1( X, Y )
% 1.12/1.48 }.
% 1.12/1.48 (21) {G0,W3,D2,L1,V0,M1} I { ! convergent_lines( skol3, skol1 ) }.
% 1.12/1.48 (22) {G0,W3,D2,L1,V0,M1} I { ! unorthogonal_lines( skol3, skol2 ) }.
% 1.12/1.48 (23) {G0,W3,D2,L1,V0,M1} I { unorthogonal_lines( skol1, skol2 ) }.
% 1.12/1.48 (34) {G1,W3,D2,L1,V0,M1} R(14,22) { convergent_lines( skol3, skol2 ) }.
% 1.12/1.48 (37) {G2,W6,D2,L2,V1,M1} R(5,34) { convergent_lines( skol2, X ),
% 1.12/1.48 convergent_lines( skol3, X ) }.
% 1.12/1.48 (40) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 1.12/1.48 convergent_lines( X, Y ) }.
% 1.12/1.48 (44) {G2,W3,D2,L1,V0,M1} R(40,21) { ! convergent_lines( skol1, skol3 ) }.
% 1.12/1.48 (46) {G3,W6,D2,L2,V1,M1} R(44,5) { ! convergent_lines( X, skol1 ),
% 1.12/1.48 convergent_lines( X, skol3 ) }.
% 1.12/1.48 (51) {G4,W6,D2,L2,V1,M2} R(46,40) { convergent_lines( skol3, X ), !
% 1.12/1.48 convergent_lines( X, skol1 ) }.
% 1.12/1.48 (55) {G5,W3,D2,L1,V0,M1} R(37,51);r(2) { convergent_lines( skol2, skol1 )
% 1.12/1.48 }.
% 1.12/1.48 (58) {G6,W3,D2,L1,V0,M1} R(55,40) { convergent_lines( skol1, skol2 ) }.
% 1.12/1.48 (165) {G1,W12,D2,L4,V3,M2} R(15,18) { convergent_lines( X, Y ), !
% 1.12/1.48 convergent_lines( Z, Y ), unorthogonal_lines( X, Z ), !
% 1.12/1.48 unorthogonal_lines( Z, Y ) }.
% 1.12/1.48 (646) {G3,W6,D2,L2,V1,M1} R(165,22);r(37) { convergent_lines( skol3, X ), !
% 1.12/1.48 unorthogonal_lines( skol2, X ) }.
% 1.12/1.48 (647) {G7,W6,D2,L2,V1,M1} R(165,23);r(58) { convergent_lines( X, skol2 ),
% 1.12/1.48 unorthogonal_lines( X, skol1 ) }.
% 1.12/1.48 (652) {G8,W3,D2,L1,V0,M1} R(647,646);r(2) { convergent_lines( skol3, skol1
% 1.12/1.48 ) }.
% 1.12/1.48 (654) {G9,W0,D0,L0,V0,M0} S(652);r(21) { }.
% 1.12/1.48
% 1.12/1.48
% 1.12/1.48 % SZS output end Refutation
% 1.12/1.48 found a proof!
% 1.12/1.48
% 1.12/1.48 *** allocated 15000 integers for termspace/termends
% 1.12/1.48
% 1.12/1.48 Unprocessed initial clauses:
% 1.12/1.48
% 1.12/1.48 (656) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 1.12/1.48 (657) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 1.12/1.48 (658) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 1.12/1.48 (659) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 1.12/1.48 , Z ), distinct_points( Y, Z ) }.
% 1.12/1.48 (660) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X, Z
% 1.12/1.48 ), distinct_lines( Y, Z ) }.
% 1.12/1.48 (661) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines(
% 1.12/1.48 X, Z ), convergent_lines( Y, Z ) }.
% 1.12/1.48 (662) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 1.12/1.48 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.12/1.48 (663) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 1.12/1.48 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 1.12/1.48 (664) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 1.12/1.48 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 1.12/1.48 (665) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 1.12/1.48 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 1.12/1.48 (666) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines(
% 1.12/1.48 Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 1.12/1.48 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 1.12/1.48 (667) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 1.12/1.48 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 1.12/1.48 (668) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ), distinct_lines
% 1.12/1.48 ( Y, Z ), apart_point_and_line( X, Z ) }.
% 1.12/1.48 (669) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), distinct_lines( Y
% 1.12/1.48 , Z ), convergent_lines( X, Z ) }.
% 1.12/1.48 (670) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines(
% 1.12/1.48 X, Y ) }.
% 1.12/1.48 (671) {G0,W12,D2,L4,V3,M4} { alpha1( X, Z ), convergent_lines( Z, Y ), !
% 1.12/1.48 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 1.12/1.48 (672) {G0,W12,D2,L4,V3,M4} { alpha1( X, Z ), unorthogonal_lines( Z, Y ), !
% 1.12/1.48 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 1.12/1.48 (673) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines( Y, X ) }.
% 1.12/1.48 (674) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), unorthogonal_lines( Y, X )
% 1.12/1.48 }.
% 1.12/1.48 (675) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( Y, X ), !
% 1.12/1.48 unorthogonal_lines( Y, X ), alpha1( X, Y ) }.
% 1.12/1.48 (676) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ), unorthogonal_lines
% 1.12/1.48 ( Z, Y ), ! convergent_lines( X, Y ) }.
% 1.12/1.48 (677) {G0,W3,D2,L1,V0,M1} { ! convergent_lines( skol3, skol1 ) }.
% 1.12/1.48 (678) {G0,W3,D2,L1,V0,M1} { ! unorthogonal_lines( skol3, skol2 ) }.
% 1.12/1.48 (679) {G0,W3,D2,L1,V0,M1} { unorthogonal_lines( skol1, skol2 ) }.
% 1.12/1.48
% 1.12/1.48
% 1.12/1.48 Total Proof:
% 1.12/1.48
% 1.12/1.48 subsumption: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 1.12/1.48 parent0: (658) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 1.12/1.48 substitution0:
% 1.12/1.48 X := X
% 1.12/1.48 end
% 1.12/1.48 permutation0:
% 1.12/1.48 0 ==> 0
% 1.12/1.48 end
% 1.12/1.48
% 1.12/1.48 subsumption: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 1.12/1.48 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 1.12/1.48 parent0: (661) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 1.12/1.48 convergent_lines( X, Z ), convergent_lines( Y, Z ) }.
% 1.12/1.48 substitution0:
% 1.12/1.48 X := X
% 1.12/1.48 Y := Y
% 1.12/1.48 Z := Z
% 1.12/1.48 end
% 1.12/1.48 permutation0:
% 1.12/1.48 0 ==> 2
% 1.12/1.48 1 ==> 0
% 1.12/1.48 2 ==> 1
% 1.12/1.48 end
% 1.12/1.48
% 1.12/1.48 subsumption: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 1.12/1.48 unorthogonal_lines( X, Y ) }.
% 1.12/1.48 parent0: (670) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ),
% 1.12/1.48 unorthogonal_lines( X, Y ) }.
% 1.12/1.48 substitution0:
% 1.12/1.48 X := X
% 1.12/1.48 Y := Y
% 1.12/1.48 end
% 1.12/1.48 permutation0:
% 1.12/1.48 0 ==> 0
% 1.12/1.48 1 ==> 1
% 1.12/1.48 end
% 1.12/1.48
% 1.12/1.48 subsumption: (15) {G0,W12,D2,L4,V3,M1} I { convergent_lines( Z, Y ), !
% 1.12/1.48 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 1.12/1.48 }.
% 1.12/1.48 parent0: (671) {G0,W12,D2,L4,V3,M4} { alpha1( X, Z ), convergent_lines( Z
% 1.12/1.48 , Y ), ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 1.12/1.48 substitution0:
% 1.12/1.48 X := X
% 1.12/1.48 Y := Y
% 1.12/1.48 Z := Z
% 1.12/1.48 end
% 1.12/1.48 permutation0:
% 1.12/1.48 0 ==> 3
% 1.12/1.48 1 ==> 0
% 1.12/1.48 2 ==> 1
% 1.12/1.48 3 ==> 2
% 1.12/1.48 end
% 1.12/1.48
% 1.12/1.48 subsumption: (18) {G0,W6,D2,L2,V2,M1} I { unorthogonal_lines( Y, X ), !
% 1.12/1.48 alpha1( X, Y ) }.
% 1.12/1.48 parent0: (674) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), unorthogonal_lines
% 1.12/1.48 ( Y, X ) }.
% 1.12/1.48 substitution0:
% 1.12/1.48 X := X
% 1.12/1.48 Y := Y
% 1.12/1.48 end
% 1.12/1.48 permutation0:
% 1.12/1.48 0 ==> 1
% 1.12/1.48 1 ==> 0
% 1.12/1.48 end
% 1.12/1.48
% 1.12/1.48 subsumption: (21) {G0,W3,D2,L1,V0,M1} I { ! convergent_lines( skol3, skol1
% 1.12/1.48 ) }.
% 1.12/1.48 parent0: (677) {G0,W3,D2,L1,V0,M1} { ! convergent_lines( skol3, skol1 )
% 1.12/1.48 }.
% 1.12/1.48 substitution0:
% 1.12/1.48 end
% 1.12/1.48 permutation0:
% 1.12/1.48 0 ==> 0
% 1.12/1.48 end
% 1.12/1.48
% 1.12/1.48 subsumption: (22) {G0,W3,D2,L1,V0,M1} I { ! unorthogonal_lines( skol3,
% 1.12/1.48 skol2 ) }.
% 1.12/1.48 parent0: (678) {G0,W3,D2,L1,V0,M1} { ! unorthogonal_lines( skol3, skol2 )
% 1.12/1.48 }.
% 1.12/1.48 substitution0:
% 1.12/1.48 end
% 1.12/1.48 permutation0:
% 1.12/1.48 0 ==> 0
% 1.12/1.48 end
% 1.12/1.48
% 1.12/1.48 subsumption: (23) {G0,W3,D2,L1,V0,M1} I { unorthogonal_lines( skol1, skol2
% 1.12/1.48 ) }.
% 1.12/1.48 parent0: (679) {G0,W3,D2,L1,V0,M1} { unorthogonal_lines( skol1, skol2 )
% 1.12/1.48 }.
% 1.12/1.48 substitution0:
% 1.12/1.48 end
% 1.12/1.48 permutation0:
% 1.12/1.48 0 ==> 0
% 1.12/1.48 end
% 1.12/1.48
% 1.12/1.48 resolution: (740) {G1,W3,D2,L1,V0,M1} { convergent_lines( skol3, skol2 )
% 1.12/1.48 }.
% 1.12/1.48 parent0[0]: (22) {G0,W3,D2,L1,V0,M1} I { ! unorthogonal_lines( skol3, skol2
% 1.12/1.48 ) }.
% 1.12/1.48 parent1[1]: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 1.12/1.48 unorthogonal_lines( X, Y ) }.
% 1.12/1.48 substitution0:
% 1.12/1.48 end
% 1.12/1.48 substitution1:
% 1.12/1.48 X := skol3
% 1.12/1.48 Y := skol2
% 1.12/1.48 end
% 1.12/1.48
% 1.12/1.48 subsumption: (34) {G1,W3,D2,L1,V0,M1} R(14,22) { convergent_lines( skol3,
% 1.12/1.48 skol2 ) }.
% 1.12/1.48 parent0: (740) {G1,W3,D2,L1,V0,M1} { convergent_lines( skol3, skol2 ) }.
% 1.12/1.48 substitution0:
% 1.12/1.48 end
% 1.12/1.48 permutation0:
% 1.12/1.48 0 ==> 0
% 1.12/1.48 end
% 1.12/1.48
% 1.12/1.48 resolution: (741) {G1,W6,D2,L2,V1,M2} { convergent_lines( skol3, X ),
% 1.12/1.48 convergent_lines( skol2, X ) }.
% 1.12/1.48 parent0[2]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 1.12/1.48 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 1.12/1.48 parent1[0]: (34) {G1,W3,D2,L1,V0,M1} R(14,22) { convergent_lines( skol3,
% 1.12/1.48 skol2 ) }.
% 1.12/1.48 substitution0:
% 1.12/1.48 X := skol3
% 1.12/1.48 Y := skol2
% 1.12/1.48 Z := X
% 1.12/1.48 end
% 1.12/1.48 substitution1:
% 1.12/1.48 end
% 1.12/1.48
% 1.12/1.48 subsumption: (37) {G2,W6,D2,L2,V1,M1} R(5,34) { convergent_lines( skol2, X
% 1.12/1.48 ), convergent_lines( skol3, X ) }.
% 1.12/1.48 parent0: (741) {G1,W6,D2,L2,V1,M2} { convergent_lines( skol3, X ),
% 1.12/1.48 convergent_lines( skol2, X ) }.
% 1.12/1.48 substitution0:
% 1.12/1.48 X := X
% 1.12/1.48 end
% 1.12/1.48 permutation0:
% 1.12/1.48 0 ==> 1
% 1.12/1.48 1 ==> 0
% 1.12/1.48 end
% 1.12/1.48
% 1.12/1.48 resolution: (742) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 1.12/1.48 convergent_lines( X, Y ) }.
% 1.12/1.48 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 1.12/1.48 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 1.12/1.48 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 1.12/1.48 substitution0:
% 1.12/1.48 X := X
% 1.12/1.48 end
% 1.12/1.48 substitution1:
% 1.12/1.48 X := X
% 1.12/1.48 Y := Y
% 1.12/1.48 Z := X
% 1.12/1.48 end
% 1.12/1.48
% 1.12/1.48 subsumption: (40) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 1.12/1.48 convergent_lines( X, Y ) }.
% 1.12/1.48 parent0: (742) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 1.12/1.48 convergent_lines( X, Y ) }.
% 1.12/1.48 substitution0:
% 1.12/1.48 X := Y
% 1.12/1.48 Y := X
% 1.12/1.48 end
% 1.12/1.48 permutation0:
% 1.12/1.48 0 ==> 1
% 1.12/1.48 1 ==> 0
% 1.12/1.48 end
% 1.12/1.48
% 1.12/1.48 resolution: (744) {G1,W3,D2,L1,V0,M1} { ! convergent_lines( skol1, skol3 )
% 1.12/1.48 }.
% 1.12/1.48 parent0[0]: (21) {G0,W3,D2,L1,V0,M1} I { ! convergent_lines( skol3, skol1 )
% 1.12/1.48 }.
% 1.12/1.48 parent1[1]: (40) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 1.12/1.48 convergent_lines( X, Y ) }.
% 1.12/1.48 substitution0:
% 1.12/1.48 end
% 1.12/1.48 substitution1:
% 1.12/1.48 X := skol3
% 1.12/1.48 Y := skol1
% 1.12/1.48 end
% 1.12/1.48
% 1.12/1.48 subsumption: (44) {G2,W3,D2,L1,V0,M1} R(40,21) { ! convergent_lines( skol1
% 1.12/1.48 , skol3 ) }.
% 1.12/1.48 parent0: (744) {G1,W3,D2,L1,V0,M1} { ! convergent_lines( skol1, skol3 )
% 1.12/1.48 }.
% 1.12/1.48 substitution0:
% 1.12/1.48 end
% 1.12/1.48 permutation0:
% 1.12/1.48 0 ==> 0
% 1.12/1.48 end
% 1.12/1.48
% 1.12/1.48 resolution: (746) {G1,W6,D2,L2,V1,M2} { convergent_lines( X, skol3 ), !
% 1.12/1.48 convergent_lines( X, skol1 ) }.
% 1.12/1.48 parent0[0]: (44) {G2,W3,D2,L1,V0,M1} R(40,21) { ! convergent_lines( skol1,
% 1.12/1.48 skol3 ) }.
% 1.12/1.48 parent1[1]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 1.12/1.48 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 1.12/1.48 substitution0:
% 1.12/1.48 end
% 1.12/1.48 substitution1:
% 1.12/1.48 X := X
% 1.12/1.48 Y := skol1
% 1.12/1.48 Z := skol3
% 1.12/1.48 end
% 1.12/1.48
% 1.12/1.48 subsumption: (46) {G3,W6,D2,L2,V1,M1} R(44,5) { ! convergent_lines( X,
% 1.12/1.48 skol1 ), convergent_lines( X, skol3 ) }.
% 1.12/1.48 parent0: (746) {G1,W6,D2,L2,V1,M2} { convergent_lines( X, skol3 ), !
% 1.12/1.48 convergent_lines( X, skol1 ) }.
% 1.12/1.48 substitution0:
% 1.12/1.48 X := X
% 1.12/1.48 end
% 1.12/1.48 permutation0:
% 1.12/1.48 0 ==> 1
% 1.12/1.48 1 ==> 0
% 1.12/1.48 end
% 1.12/1.48
% 1.12/1.48 resolution: (748) {G2,W6,D2,L2,V1,M2} { convergent_lines( skol3, X ), !
% 1.12/1.48 convergent_lines( X, skol1 ) }.
% 1.12/1.48 parent0[0]: (40) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 1.12/1.48 convergent_lines( X, Y ) }.
% 1.12/1.48 parent1[1]: (46) {G3,W6,D2,L2,V1,M1} R(44,5) { ! convergent_lines( X, skol1
% 1.12/1.48 ), convergent_lines( X, skol3 ) }.
% 1.12/1.48 substitution0:
% 1.12/1.48 X := skol3
% 1.12/1.48 Y := X
% 1.12/1.48 end
% 1.12/1.48 substitution1:
% 1.12/1.48 X := X
% 1.12/1.48 end
% 1.12/1.48
% 1.12/1.48 subsumption: (51) {G4,W6,D2,L2,V1,M2} R(46,40) { convergent_lines( skol3, X
% 1.12/1.48 ), ! convergent_lines( X, skol1 ) }.
% 1.12/1.48 parent0: (748) {G2,W6,D2,L2,V1,M2} { convergent_lines( skol3, X ), !
% 1.12/1.48 convergent_lines( X, skol1 ) }.
% 1.12/1.48 substitution0:
% 1.12/1.48 X := X
% 1.12/1.48 end
% 1.12/1.48 permutation0:
% 1.12/1.48 0 ==> 0
% 1.12/1.48 1 ==> 1
% 1.12/1.48 end
% 1.12/1.48
% 1.12/1.48 resolution: (750) {G3,W6,D2,L2,V0,M2} { convergent_lines( skol3, skol3 ),
% 1.12/1.48 convergent_lines( skol2, skol1 ) }.
% 1.12/1.48 parent0[1]: (51) {G4,W6,D2,L2,V1,M2} R(46,40) { convergent_lines( skol3, X
% 1.12/1.48 ), ! convergent_lines( X, skol1 ) }.
% 1.12/1.48 parent1[1]: (37) {G2,W6,D2,L2,V1,M1} R(5,34) { convergent_lines( skol2, X )
% 1.12/1.48 , convergent_lines( skol3, X ) }.
% 1.12/1.48 substitution0:
% 1.12/1.48 X := skol3
% 1.12/1.48 end
% 1.12/1.48 substitution1:
% 1.12/1.48 X := skol1
% 1.12/1.48 end
% 1.12/1.48
% 1.12/1.48 resolution: (751) {G1,W3,D2,L1,V0,M1} { convergent_lines( skol2, skol1 )
% 1.12/1.48 }.
% 1.12/1.48 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 1.12/1.48 parent1[0]: (750) {G3,W6,D2,L2,V0,M2} { convergent_lines( skol3, skol3 ),
% 1.12/1.48 convergent_lines( skol2, skol1 ) }.
% 1.12/1.48 substitution0:
% 1.12/1.48 X := skol3
% 1.12/1.48 end
% 1.12/1.48 substitution1:
% 1.12/1.48 end
% 1.12/1.48
% 1.12/1.48 subsumption: (55) {G5,W3,D2,L1,V0,M1} R(37,51);r(2) { convergent_lines(
% 1.12/1.48 skol2, skol1 ) }.
% 1.12/1.48 parent0: (751) {G1,W3,D2,L1,V0,M1} { convergent_lines( skol2, skol1 ) }.
% 1.12/1.48 substitution0:
% 1.12/1.48 end
% 1.12/1.48 permutation0:
% 1.12/1.48 0 ==> 0
% 1.12/1.48 end
% 1.12/1.48
% 1.12/1.48 resolution: (752) {G2,W3,D2,L1,V0,M1} { convergent_lines( skol1, skol2 )
% 1.12/1.48 }.
% 1.12/1.48 parent0[0]: (40) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 1.12/1.48 convergent_lines( X, Y ) }.
% 1.12/1.48 parent1[0]: (55) {G5,W3,D2,L1,V0,M1} R(37,51);r(2) { convergent_lines(
% 1.12/1.48 skol2, skol1 ) }.
% 1.12/1.48 substitution0:
% 1.12/1.48 X := skol1
% 1.12/1.48 Y := skol2
% 1.12/1.48 end
% 1.12/1.48 substitution1:
% 1.12/1.48 end
% 1.12/1.48
% 1.12/1.48 subsumption: (58) {G6,W3,D2,L1,V0,M1} R(55,40) { convergent_lines( skol1,
% 1.12/1.48 skol2 ) }.
% 1.12/1.48 parent0: (752) {G2,W3,D2,L1,V0,M1} { convergent_lines( skol1, skol2 ) }.
% 1.12/1.48 substitution0:
% 1.12/1.48 end
% 1.12/1.48 permutation0:
% 1.12/1.48 0 ==> 0
% 1.12/1.48 end
% 1.12/1.48
% 1.12/1.48 resolution: (754) {G1,W12,D2,L4,V3,M4} { unorthogonal_lines( X, Y ),
% 1.12/1.48 convergent_lines( X, Z ), ! convergent_lines( Y, Z ), !
% 1.12/1.48 unorthogonal_lines( Y, Z ) }.
% 1.12/1.48 parent0[1]: (18) {G0,W6,D2,L2,V2,M1} I { unorthogonal_lines( Y, X ), !
% 1.12/1.48 alpha1( X, Y ) }.
% 1.12/1.48 parent1[3]: (15) {G0,W12,D2,L4,V3,M1} I { convergent_lines( Z, Y ), !
% 1.12/1.48 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 1.12/1.48 }.
% 1.12/1.48 substitution0:
% 1.12/1.48 X := Y
% 1.12/1.48 Y := X
% 1.12/1.48 end
% 1.12/1.48 substitution1:
% 1.12/1.48 X := Y
% 1.12/1.48 Y := Z
% 1.12/1.48 Z := X
% 1.12/1.48 end
% 1.12/1.48
% 1.12/1.48 subsumption: (165) {G1,W12,D2,L4,V3,M2} R(15,18) { convergent_lines( X, Y )
% 1.12/1.48 , ! convergent_lines( Z, Y ), unorthogonal_lines( X, Z ), !
% 1.12/1.48 unorthogonal_lines( Z, Y ) }.
% 1.12/1.48 parent0: (754) {G1,W12,D2,L4,V3,M4} { unorthogonal_lines( X, Y ),
% 1.12/1.48 convergent_lines( X, Z ), ! convergent_lines( Y, Z ), !
% 1.12/1.48 unorthogonal_lines( Y, Z ) }.
% 1.12/1.48 substitution0:
% 1.12/1.48 X := X
% 1.12/1.48 Y := Z
% 1.12/1.48 Z := Y
% 1.12/1.48 end
% 1.12/1.48 permutation0:
% 1.12/1.48 0 ==> 2
% 1.12/1.48 1 ==> 0
% 1.12/1.48 2 ==> 1
% 1.12/1.48 3 ==> 3
% 1.12/1.48 end
% 1.12/1.48
% 1.12/1.48 resolution: (755) {G1,W9,D2,L3,V1,M3} { convergent_lines( skol3, X ), !
% 1.12/1.48 convergent_lines( skol2, X ), ! unorthogonal_lines( skol2, X ) }.
% 1.12/1.48 parent0[0]: (22) {G0,W3,D2,L1,V0,M1} I { ! unorthogonal_lines( skol3, skol2
% 1.12/1.48 ) }.
% 1.12/1.48 parent1[2]: (165) {G1,W12,D2,L4,V3,M2} R(15,18) { convergent_lines( X, Y )
% 1.12/1.48 , ! convergent_lines( Z, Y ), unorthogonal_lines( X, Z ), !
% 1.12/1.48 unorthogonal_lines( Z, Y ) }.
% 1.12/1.48 substitution0:
% 1.12/1.48 end
% 1.12/1.48 substitution1:
% 1.12/1.48 X := skol3
% 1.12/1.48 Y := X
% 1.12/1.48 Z := skol2
% 1.12/1.48 end
% 1.12/1.48
% 1.12/1.48 resolution: (756) {G2,W9,D2,L3,V1,M3} { convergent_lines( skol3, X ), !
% 1.12/1.48 unorthogonal_lines( skol2, X ), convergent_lines( skol3, X ) }.
% 1.12/1.48 parent0[1]: (755) {G1,W9,D2,L3,V1,M3} { convergent_lines( skol3, X ), !
% 1.12/1.48 convergent_lines( skol2, X ), ! unorthogonal_lines( skol2, X ) }.
% 1.12/1.48 parent1[0]: (37) {G2,W6,D2,L2,V1,M1} R(5,34) { convergent_lines( skol2, X )
% 1.12/1.48 , convergent_lines( skol3, X ) }.
% 1.12/1.48 substitution0:
% 1.12/1.48 X := X
% 1.12/1.48 end
% 1.12/1.48 substitution1:
% 1.12/1.48 X := X
% 1.12/1.48 end
% 1.12/1.48
% 1.12/1.48 factor: (757) {G2,W6,D2,L2,V1,M2} { convergent_lines( skol3, X ), !
% 1.12/1.48 unorthogonal_lines( skol2, X ) }.
% 1.12/1.48 parent0[0, 2]: (756) {G2,W9,D2,L3,V1,M3} { convergent_lines( skol3, X ), !
% 1.12/1.48 unorthogonal_lines( skol2, X ), convergent_lines( skol3, X ) }.
% 1.12/1.48 substitution0:
% 1.12/1.48 X := X
% 1.12/1.48 end
% 1.12/1.48
% 1.12/1.48 subsumption: (646) {G3,W6,D2,L2,V1,M1} R(165,22);r(37) { convergent_lines(
% 1.12/1.48 skol3, X ), ! unorthogonal_lines( skol2, X ) }.
% 1.12/1.48 parent0: (757) {G2,W6,D2,L2,V1,M2} { convergent_lines( skol3, X ), !
% 1.12/1.48 unorthogonal_lines( skol2, X ) }.
% 1.12/1.48 substitution0:
% 1.12/1.48 X := X
% 1.12/1.48 end
% 1.12/1.48 permutation0:
% 1.12/1.48 0 ==> 0
% 1.12/1.48 1 ==> 1
% 1.12/1.48 end
% 1.12/1.48
% 1.12/1.48 resolution: (758) {G1,W9,D2,L3,V1,M3} { convergent_lines( X, skol2 ), !
% 1.12/1.48 convergent_lines( skol1, skol2 ), unorthogonal_lines( X, skol1 ) }.
% 1.12/1.48 parent0[3]: (165) {G1,W12,D2,L4,V3,M2} R(15,18) { convergent_lines( X, Y )
% 1.12/1.48 , ! convergent_lines( Z, Y ), unorthogonal_lines( X, Z ), !
% 1.12/1.48 unorthogonal_lines( Z, Y ) }.
% 1.12/1.48 parent1[0]: (23) {G0,W3,D2,L1,V0,M1} I { unorthogonal_lines( skol1, skol2 )
% 1.12/1.48 }.
% 1.12/1.48 substitution0:
% 1.12/1.48 X := X
% 1.12/1.48 Y := skol2
% 1.12/1.48 Z := skol1
% 1.12/1.48 end
% 1.12/1.48 substitution1:
% 1.12/1.48 end
% 1.12/1.48
% 1.12/1.48 resolution: (759) {G2,W6,D2,L2,V1,M2} { convergent_lines( X, skol2 ),
% 1.12/1.48 unorthogonal_lines( X, skol1 ) }.
% 1.12/1.48 parent0[1]: (758) {G1,W9,D2,L3,V1,M3} { convergent_lines( X, skol2 ), !
% 1.12/1.48 convergent_lines( skol1, skol2 ), unorthogonal_lines( X, skol1 ) }.
% 1.12/1.48 parent1[0]: (58) {G6,W3,D2,L1,V0,M1} R(55,40) { convergent_lines( skol1,
% 1.12/1.48 skol2 ) }.
% 1.12/1.48 substitution0:
% 1.12/1.48 X := X
% 1.12/1.48 end
% 1.12/1.48 substitution1:
% 1.12/1.48 end
% 1.12/1.48
% 1.12/1.48 subsumption: (647) {G7,W6,D2,L2,V1,M1} R(165,23);r(58) { convergent_lines(
% 1.12/1.49 X, skol2 ), unorthogonal_lines( X, skol1 ) }.
% 1.12/1.49 parent0: (759) {G2,W6,D2,L2,V1,M2} { convergent_lines( X, skol2 ),
% 1.12/1.49 unorthogonal_lines( X, skol1 ) }.
% 1.12/1.49 substitution0:
% 1.12/1.49 X := X
% 1.12/1.49 end
% 1.12/1.49 permutation0:
% 1.12/1.49 0 ==> 0
% 1.12/1.49 1 ==> 1
% 1.12/1.49 end
% 1.12/1.49
% 1.12/1.49 resolution: (760) {G4,W6,D2,L2,V0,M2} { convergent_lines( skol3, skol1 ),
% 1.12/1.49 convergent_lines( skol2, skol2 ) }.
% 1.12/1.49 parent0[1]: (646) {G3,W6,D2,L2,V1,M1} R(165,22);r(37) { convergent_lines(
% 1.12/1.49 skol3, X ), ! unorthogonal_lines( skol2, X ) }.
% 1.12/1.49 parent1[1]: (647) {G7,W6,D2,L2,V1,M1} R(165,23);r(58) { convergent_lines( X
% 1.12/1.49 , skol2 ), unorthogonal_lines( X, skol1 ) }.
% 1.12/1.49 substitution0:
% 1.12/1.49 X := skol1
% 1.12/1.49 end
% 1.12/1.49 substitution1:
% 1.12/1.49 X := skol2
% 1.12/1.49 end
% 1.12/1.49
% 1.12/1.49 resolution: (761) {G1,W3,D2,L1,V0,M1} { convergent_lines( skol3, skol1 )
% 1.12/1.49 }.
% 1.12/1.49 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 1.12/1.49 parent1[1]: (760) {G4,W6,D2,L2,V0,M2} { convergent_lines( skol3, skol1 ),
% 1.12/1.49 convergent_lines( skol2, skol2 ) }.
% 1.12/1.49 substitution0:
% 1.12/1.49 X := skol2
% 1.12/1.49 end
% 1.12/1.49 substitution1:
% 1.12/1.49 end
% 1.12/1.49
% 1.12/1.49 subsumption: (652) {G8,W3,D2,L1,V0,M1} R(647,646);r(2) { convergent_lines(
% 1.12/1.49 skol3, skol1 ) }.
% 1.12/1.49 parent0: (761) {G1,W3,D2,L1,V0,M1} { convergent_lines( skol3, skol1 ) }.
% 1.12/1.49 substitution0:
% 1.12/1.49 end
% 1.12/1.49 permutation0:
% 1.12/1.49 0 ==> 0
% 1.12/1.49 end
% 1.12/1.49
% 1.12/1.49 resolution: (762) {G1,W0,D0,L0,V0,M0} { }.
% 1.12/1.49 parent0[0]: (21) {G0,W3,D2,L1,V0,M1} I { ! convergent_lines( skol3, skol1 )
% 1.12/1.49 }.
% 1.12/1.49 parent1[0]: (652) {G8,W3,D2,L1,V0,M1} R(647,646);r(2) { convergent_lines(
% 1.12/1.49 skol3, skol1 ) }.
% 1.12/1.49 substitution0:
% 1.12/1.49 end
% 1.12/1.49 substitution1:
% 1.12/1.49 end
% 1.12/1.49
% 1.12/1.49 subsumption: (654) {G9,W0,D0,L0,V0,M0} S(652);r(21) { }.
% 1.12/1.49 parent0: (762) {G1,W0,D0,L0,V0,M0} { }.
% 1.12/1.49 substitution0:
% 1.12/1.49 end
% 1.12/1.49 permutation0:
% 1.12/1.49 end
% 1.12/1.49
% 1.12/1.49 Proof check complete!
% 1.12/1.49
% 1.12/1.49 Memory use:
% 1.12/1.49
% 1.12/1.49 space for terms: 9877
% 1.12/1.49 space for clauses: 23266
% 1.12/1.49
% 1.12/1.49
% 1.12/1.49 clauses generated: 27556
% 1.12/1.49 clauses kept: 655
% 1.12/1.49 clauses selected: 243
% 1.12/1.49 clauses deleted: 1
% 1.12/1.49 clauses inuse deleted: 0
% 1.12/1.49
% 1.12/1.49 subsentry: 355214
% 1.12/1.49 literals s-matched: 223240
% 1.12/1.49 literals matched: 223210
% 1.12/1.49 full subsumption: 197719
% 1.12/1.49
% 1.12/1.49 checksum: -313340
% 1.12/1.49
% 1.12/1.49
% 1.12/1.49 Bliksem ended
%------------------------------------------------------------------------------