TSTP Solution File: GEO213+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO213+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n017.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 02:52:49 EDT 2022
% Result : Theorem 1.19s 1.56s
% Output : Refutation 1.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO213+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : bliksem %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Fri Jun 17 23:41:12 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.19/1.56 *** allocated 10000 integers for termspace/termends
% 1.19/1.56 *** allocated 10000 integers for clauses
% 1.19/1.56 *** allocated 10000 integers for justifications
% 1.19/1.56 Bliksem 1.12
% 1.19/1.56
% 1.19/1.56
% 1.19/1.56 Automatic Strategy Selection
% 1.19/1.56
% 1.19/1.56
% 1.19/1.56 Clauses:
% 1.19/1.56
% 1.19/1.56 { ! distinct_points( X, X ) }.
% 1.19/1.56 { ! distinct_lines( X, X ) }.
% 1.19/1.56 { ! convergent_lines( X, X ) }.
% 1.19/1.56 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 1.19/1.56 ) }.
% 1.19/1.56 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 1.19/1.56 }.
% 1.19/1.56 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 1.19/1.56 , Z ) }.
% 1.19/1.56 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 1.19/1.56 , Y ) ) }.
% 1.19/1.56 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 1.19/1.56 , Y ) ) }.
% 1.19/1.56 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 1.19/1.56 , Y ), X ) }.
% 1.19/1.56 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 1.19/1.56 , Y ), Y ) }.
% 1.19/1.56 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 1.19/1.56 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 1.19/1.56 apart_point_and_line( Y, T ) }.
% 1.19/1.56 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 1.19/1.56 apart_point_and_line( Z, Y ) }.
% 1.19/1.56 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 1.19/1.56 apart_point_and_line( X, Z ) }.
% 1.19/1.56 { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X,
% 1.19/1.56 Z ) }.
% 1.19/1.56 { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 1.19/1.56 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 1.19/1.56 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 1.19/1.56 apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 1.19/1.56 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 1.19/1.56 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 1.19/1.56 , convergent_lines( Y, Z ) }.
% 1.19/1.56 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 1.19/1.56 , unorthogonal_lines( Y, Z ) }.
% 1.19/1.56 { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 1.19/1.56 { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 1.19/1.56 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 1.19/1.56 }.
% 1.19/1.56 { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 1.19/1.56 { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 1.19/1.56 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 1.19/1.56 apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ),
% 1.19/1.56 unorthogonal_lines( Y, T ) }.
% 1.19/1.56 { unorthogonal_lines( skol1, skol2 ) }.
% 1.19/1.56 { ! distinct_lines( skol1, skol3 ) }.
% 1.19/1.56 { ! unorthogonal_lines( skol2, skol3 ) }.
% 1.19/1.56
% 1.19/1.56 percentage equality = 0.000000, percentage horn = 0.586207
% 1.19/1.56 This a non-horn, non-equality problem
% 1.19/1.56
% 1.19/1.56
% 1.19/1.56 Options Used:
% 1.19/1.56
% 1.19/1.56 useres = 1
% 1.19/1.56 useparamod = 0
% 1.19/1.56 useeqrefl = 0
% 1.19/1.56 useeqfact = 0
% 1.19/1.56 usefactor = 1
% 1.19/1.56 usesimpsplitting = 0
% 1.19/1.56 usesimpdemod = 0
% 1.19/1.56 usesimpres = 3
% 1.19/1.56
% 1.19/1.56 resimpinuse = 1000
% 1.19/1.56 resimpclauses = 20000
% 1.19/1.56 substype = standard
% 1.19/1.56 backwardsubs = 1
% 1.19/1.56 selectoldest = 5
% 1.19/1.56
% 1.19/1.56 litorderings [0] = split
% 1.19/1.56 litorderings [1] = liftord
% 1.19/1.56
% 1.19/1.56 termordering = none
% 1.19/1.56
% 1.19/1.56 litapriori = 1
% 1.19/1.56 termapriori = 0
% 1.19/1.56 litaposteriori = 0
% 1.19/1.56 termaposteriori = 0
% 1.19/1.56 demodaposteriori = 0
% 1.19/1.56 ordereqreflfact = 0
% 1.19/1.56
% 1.19/1.56 litselect = none
% 1.19/1.56
% 1.19/1.56 maxweight = 15
% 1.19/1.56 maxdepth = 30000
% 1.19/1.56 maxlength = 115
% 1.19/1.56 maxnrvars = 195
% 1.19/1.56 excuselevel = 1
% 1.19/1.56 increasemaxweight = 1
% 1.19/1.56
% 1.19/1.56 maxselected = 10000000
% 1.19/1.56 maxnrclauses = 10000000
% 1.19/1.56
% 1.19/1.56 showgenerated = 0
% 1.19/1.56 showkept = 0
% 1.19/1.56 showselected = 0
% 1.19/1.56 showdeleted = 0
% 1.19/1.56 showresimp = 1
% 1.19/1.56 showstatus = 2000
% 1.19/1.56
% 1.19/1.56 prologoutput = 0
% 1.19/1.56 nrgoals = 5000000
% 1.19/1.56 totalproof = 1
% 1.19/1.56
% 1.19/1.56 Symbols occurring in the translation:
% 1.19/1.56
% 1.19/1.56 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.19/1.56 . [1, 2] (w:1, o:23, a:1, s:1, b:0),
% 1.19/1.56 ! [4, 1] (w:0, o:18, a:1, s:1, b:0),
% 1.19/1.56 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.19/1.56 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.19/1.56 distinct_points [36, 2] (w:1, o:48, a:1, s:1, b:0),
% 1.19/1.56 distinct_lines [37, 2] (w:1, o:49, a:1, s:1, b:0),
% 1.19/1.56 convergent_lines [38, 2] (w:1, o:47, a:1, s:1, b:0),
% 1.19/1.56 line_connecting [41, 2] (w:1, o:50, a:1, s:1, b:0),
% 1.19/1.56 apart_point_and_line [42, 2] (w:1, o:51, a:1, s:1, b:0),
% 1.19/1.56 intersection_point [43, 2] (w:1, o:52, a:1, s:1, b:0),
% 1.19/1.56 parallel_through_point [46, 2] (w:1, o:54, a:1, s:1, b:0),
% 1.19/1.56 unorthogonal_lines [49, 2] (w:1, o:55, a:1, s:1, b:0),
% 1.19/1.56 orthogonal_through_point [52, 2] (w:1, o:53, a:1, s:1, b:0),
% 1.19/1.56 alpha1 [53, 2] (w:1, o:56, a:1, s:1, b:0),
% 1.19/1.56 skol1 [54, 0] (w:1, o:15, a:1, s:1, b:0),
% 1.19/1.56 skol2 [55, 0] (w:1, o:16, a:1, s:1, b:0),
% 1.19/1.56 skol3 [56, 0] (w:1, o:17, a:1, s:1, b:0).
% 1.19/1.56
% 1.19/1.56
% 1.19/1.56 Starting Search:
% 1.19/1.56
% 1.19/1.56 *** allocated 15000 integers for clauses
% 1.19/1.56 *** allocated 22500 integers for clauses
% 1.19/1.56 *** allocated 33750 integers for clauses
% 1.19/1.56 *** allocated 50625 integers for clauses
% 1.19/1.56 *** allocated 15000 integers for termspace/termends
% 1.19/1.56 Resimplifying inuse:
% 1.19/1.56 Done
% 1.19/1.56
% 1.19/1.56 *** allocated 22500 integers for termspace/termends
% 1.19/1.56 *** allocated 75937 integers for clauses
% 1.19/1.56 *** allocated 33750 integers for termspace/termends
% 1.19/1.56 *** allocated 113905 integers for clauses
% 1.19/1.56
% 1.19/1.56 Intermediate Status:
% 1.19/1.56 Generated: 22658
% 1.19/1.56 Kept: 2000
% 1.19/1.56 Inuse: 340
% 1.19/1.56 Deleted: 0
% 1.19/1.56 Deletedinuse: 0
% 1.19/1.56
% 1.19/1.56 Resimplifying inuse:
% 1.19/1.56 Done
% 1.19/1.56
% 1.19/1.56 *** allocated 50625 integers for termspace/termends
% 1.19/1.56 *** allocated 170857 integers for clauses
% 1.19/1.56 Resimplifying inuse:
% 1.19/1.56 Done
% 1.19/1.56
% 1.19/1.56 *** allocated 75937 integers for termspace/termends
% 1.19/1.56
% 1.19/1.56 Intermediate Status:
% 1.19/1.56 Generated: 35661
% 1.19/1.56 Kept: 4010
% 1.19/1.56 Inuse: 468
% 1.19/1.56 Deleted: 0
% 1.19/1.56 Deletedinuse: 0
% 1.19/1.56
% 1.19/1.56 Resimplifying inuse:
% 1.19/1.56 Done
% 1.19/1.56
% 1.19/1.56 *** allocated 256285 integers for clauses
% 1.19/1.56
% 1.19/1.56 Bliksems!, er is een bewijs:
% 1.19/1.56 % SZS status Theorem
% 1.19/1.56 % SZS output start Refutation
% 1.19/1.56
% 1.19/1.56 (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 1.19/1.56 (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 1.19/1.56 (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 1.19/1.56 , ! distinct_lines( X, Y ) }.
% 1.19/1.56 (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), convergent_lines( Y,
% 1.19/1.56 Z ), ! convergent_lines( X, Y ) }.
% 1.19/1.56 (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ), convergent_lines(
% 1.19/1.56 X, Z ), distinct_lines( Y, Z ) }.
% 1.19/1.56 (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), unorthogonal_lines(
% 1.19/1.56 X, Y ) }.
% 1.19/1.56 (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 1.19/1.56 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 1.19/1.56 }.
% 1.19/1.56 (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! alpha1( X, Y ) }.
% 1.19/1.56 (26) {G0,W3,D2,L1,V0,M1} I { unorthogonal_lines( skol1, skol2 ) }.
% 1.19/1.56 (27) {G0,W3,D2,L1,V0,M1} I { ! distinct_lines( skol1, skol3 ) }.
% 1.19/1.56 (28) {G0,W3,D2,L1,V0,M1} I { ! unorthogonal_lines( skol2, skol3 ) }.
% 1.19/1.56 (36) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 1.19/1.56 ( X, Y ) }.
% 1.19/1.56 (39) {G2,W3,D2,L1,V0,M1} R(36,27) { ! distinct_lines( skol3, skol1 ) }.
% 1.19/1.56 (48) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 1.19/1.56 convergent_lines( X, Y ) }.
% 1.19/1.56 (55) {G1,W3,D2,L1,V0,M1} R(17,28) { convergent_lines( skol2, skol3 ) }.
% 1.19/1.56 (57) {G2,W6,D2,L2,V1,M1} R(55,5) { convergent_lines( skol2, X ),
% 1.19/1.56 convergent_lines( skol3, X ) }.
% 1.19/1.56 (61) {G3,W6,D2,L2,V1,M2} R(57,48) { convergent_lines( X, skol3 ),
% 1.19/1.56 convergent_lines( skol2, X ) }.
% 1.19/1.56 (161) {G3,W6,D2,L2,V1,M1} R(13,39) { convergent_lines( X, skol1 ), !
% 1.19/1.56 convergent_lines( X, skol3 ) }.
% 1.19/1.56 (171) {G4,W3,D2,L1,V0,M1} R(161,61);r(2) { convergent_lines( skol2, skol1 )
% 1.19/1.56 }.
% 1.19/1.56 (173) {G4,W6,D2,L2,V1,M2} R(161,48) { ! convergent_lines( skol3, X ),
% 1.19/1.56 convergent_lines( X, skol1 ) }.
% 1.19/1.56 (176) {G5,W3,D2,L1,V0,M1} R(171,48) { convergent_lines( skol1, skol2 ) }.
% 1.19/1.56 (206) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y ),
% 1.19/1.56 convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 1.19/1.56 unorthogonal_lines( Y, Z ) }.
% 1.19/1.56 (212) {G5,W9,D2,L3,V2,M2} R(173,5) { convergent_lines( X, skol1 ), !
% 1.19/1.56 convergent_lines( Y, skol3 ), convergent_lines( Y, X ) }.
% 1.19/1.56 (216) {G6,W3,D2,L1,V0,M1} F(212);r(2) { ! convergent_lines( skol1, skol3 )
% 1.19/1.56 }.
% 1.19/1.56 (4678) {G6,W6,D2,L2,V1,M1} R(206,26);r(176) { convergent_lines( skol1, X )
% 1.19/1.56 , unorthogonal_lines( skol2, X ) }.
% 1.19/1.56 (4683) {G7,W0,D0,L0,V0,M0} R(4678,28);r(216) { }.
% 1.19/1.56
% 1.19/1.56
% 1.19/1.56 % SZS output end Refutation
% 1.19/1.56 found a proof!
% 1.19/1.56
% 1.19/1.56
% 1.19/1.56 Unprocessed initial clauses:
% 1.19/1.56
% 1.19/1.56 (4685) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 1.19/1.56 (4686) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 1.19/1.56 (4687) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 1.19/1.56 (4688) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 1.19/1.56 , Z ), distinct_points( Y, Z ) }.
% 1.19/1.56 (4689) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X,
% 1.19/1.56 Z ), distinct_lines( Y, Z ) }.
% 1.19/1.56 (4690) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines
% 1.19/1.56 ( X, Z ), convergent_lines( Y, Z ) }.
% 1.19/1.56 (4691) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 1.19/1.56 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.19/1.56 (4692) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 1.19/1.56 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 1.19/1.56 (4693) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 1.19/1.56 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 1.19/1.56 (4694) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 1.19/1.56 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 1.19/1.56 (4695) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines
% 1.19/1.56 ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 1.19/1.56 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 1.19/1.56 (4696) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 1.19/1.56 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 1.19/1.56 (4697) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 1.19/1.56 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 1.19/1.56 (4698) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), distinct_lines( Y
% 1.19/1.56 , Z ), convergent_lines( X, Z ) }.
% 1.19/1.56 (4699) {G0,W5,D3,L1,V2,M1} { ! convergent_lines( parallel_through_point( Y
% 1.19/1.56 , X ), Y ) }.
% 1.19/1.56 (4700) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 1.19/1.56 parallel_through_point( Y, X ) ) }.
% 1.19/1.56 (4701) {G0,W12,D2,L4,V3,M4} { ! distinct_lines( X, Y ),
% 1.19/1.56 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 1.19/1.56 convergent_lines( X, Y ) }.
% 1.19/1.56 (4702) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines
% 1.19/1.56 ( X, Y ) }.
% 1.19/1.56 (4703) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 1.19/1.56 unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 1.19/1.56 (4704) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 1.19/1.56 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 1.19/1.56 }.
% 1.19/1.56 (4705) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines( X, Y )
% 1.19/1.56 }.
% 1.19/1.56 (4706) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 1.19/1.56 }.
% 1.19/1.56 (4707) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( X, Y ), !
% 1.19/1.56 unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 1.19/1.56 (4708) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines(
% 1.19/1.56 orthogonal_through_point( Y, X ), Y ) }.
% 1.19/1.56 (4709) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 1.19/1.56 orthogonal_through_point( Y, X ) ) }.
% 1.19/1.56 (4710) {G0,W15,D2,L5,V4,M5} { ! distinct_lines( X, Y ),
% 1.19/1.56 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 1.19/1.56 unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 1.19/1.56 (4711) {G0,W3,D2,L1,V0,M1} { unorthogonal_lines( skol1, skol2 ) }.
% 1.19/1.56 (4712) {G0,W3,D2,L1,V0,M1} { ! distinct_lines( skol1, skol3 ) }.
% 1.19/1.56 (4713) {G0,W3,D2,L1,V0,M1} { ! unorthogonal_lines( skol2, skol3 ) }.
% 1.19/1.56
% 1.19/1.56
% 1.19/1.56 Total Proof:
% 1.19/1.56
% 1.19/1.56 subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 1.19/1.56 parent0: (4686) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 X := X
% 1.19/1.56 end
% 1.19/1.56 permutation0:
% 1.19/1.56 0 ==> 0
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 subsumption: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 1.19/1.56 parent0: (4687) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 X := X
% 1.19/1.56 end
% 1.19/1.56 permutation0:
% 1.19/1.56 0 ==> 0
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 1.19/1.56 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 1.19/1.56 parent0: (4689) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ),
% 1.19/1.56 distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 X := X
% 1.19/1.56 Y := Y
% 1.19/1.56 Z := Z
% 1.19/1.56 end
% 1.19/1.56 permutation0:
% 1.19/1.56 0 ==> 2
% 1.19/1.56 1 ==> 0
% 1.19/1.56 2 ==> 1
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 subsumption: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 1.19/1.56 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 1.19/1.56 parent0: (4690) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 1.19/1.56 convergent_lines( X, Z ), convergent_lines( Y, Z ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 X := X
% 1.19/1.56 Y := Y
% 1.19/1.56 Z := Z
% 1.19/1.56 end
% 1.19/1.56 permutation0:
% 1.19/1.56 0 ==> 2
% 1.19/1.56 1 ==> 0
% 1.19/1.56 2 ==> 1
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 subsumption: (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ),
% 1.19/1.56 convergent_lines( X, Z ), distinct_lines( Y, Z ) }.
% 1.19/1.56 parent0: (4698) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 1.19/1.56 distinct_lines( Y, Z ), convergent_lines( X, Z ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 X := X
% 1.19/1.56 Y := Y
% 1.19/1.56 Z := Z
% 1.19/1.56 end
% 1.19/1.56 permutation0:
% 1.19/1.56 0 ==> 0
% 1.19/1.56 1 ==> 2
% 1.19/1.56 2 ==> 1
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 subsumption: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 1.19/1.56 unorthogonal_lines( X, Y ) }.
% 1.19/1.56 parent0: (4702) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ),
% 1.19/1.56 unorthogonal_lines( X, Y ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 X := X
% 1.19/1.56 Y := Y
% 1.19/1.56 end
% 1.19/1.56 permutation0:
% 1.19/1.56 0 ==> 0
% 1.19/1.56 1 ==> 1
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 subsumption: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 1.19/1.56 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 1.19/1.56 }.
% 1.19/1.56 parent0: (4704) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 1.19/1.56 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 1.19/1.56 }.
% 1.19/1.56 substitution0:
% 1.19/1.56 X := X
% 1.19/1.56 Y := Y
% 1.19/1.56 Z := Z
% 1.19/1.56 end
% 1.19/1.56 permutation0:
% 1.19/1.56 0 ==> 0
% 1.19/1.56 1 ==> 1
% 1.19/1.56 2 ==> 3
% 1.19/1.56 3 ==> 2
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 subsumption: (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 1.19/1.56 alpha1( X, Y ) }.
% 1.19/1.56 parent0: (4705) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines(
% 1.19/1.56 X, Y ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 X := X
% 1.19/1.56 Y := Y
% 1.19/1.56 end
% 1.19/1.56 permutation0:
% 1.19/1.56 0 ==> 1
% 1.19/1.56 1 ==> 0
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 subsumption: (26) {G0,W3,D2,L1,V0,M1} I { unorthogonal_lines( skol1, skol2
% 1.19/1.56 ) }.
% 1.19/1.56 parent0: (4711) {G0,W3,D2,L1,V0,M1} { unorthogonal_lines( skol1, skol2 )
% 1.19/1.56 }.
% 1.19/1.56 substitution0:
% 1.19/1.56 end
% 1.19/1.56 permutation0:
% 1.19/1.56 0 ==> 0
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 subsumption: (27) {G0,W3,D2,L1,V0,M1} I { ! distinct_lines( skol1, skol3 )
% 1.19/1.56 }.
% 1.19/1.56 parent0: (4712) {G0,W3,D2,L1,V0,M1} { ! distinct_lines( skol1, skol3 ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 end
% 1.19/1.56 permutation0:
% 1.19/1.56 0 ==> 0
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 subsumption: (28) {G0,W3,D2,L1,V0,M1} I { ! unorthogonal_lines( skol2,
% 1.19/1.56 skol3 ) }.
% 1.19/1.56 parent0: (4713) {G0,W3,D2,L1,V0,M1} { ! unorthogonal_lines( skol2, skol3 )
% 1.19/1.56 }.
% 1.19/1.56 substitution0:
% 1.19/1.56 end
% 1.19/1.56 permutation0:
% 1.19/1.56 0 ==> 0
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 resolution: (4794) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 1.19/1.56 distinct_lines( X, Y ) }.
% 1.19/1.56 parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 1.19/1.56 parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 1.19/1.56 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 X := X
% 1.19/1.56 end
% 1.19/1.56 substitution1:
% 1.19/1.56 X := X
% 1.19/1.56 Y := Y
% 1.19/1.56 Z := X
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 subsumption: (36) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 1.19/1.56 distinct_lines( X, Y ) }.
% 1.19/1.56 parent0: (4794) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 1.19/1.56 distinct_lines( X, Y ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 X := Y
% 1.19/1.56 Y := X
% 1.19/1.56 end
% 1.19/1.56 permutation0:
% 1.19/1.56 0 ==> 1
% 1.19/1.56 1 ==> 0
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 resolution: (4796) {G1,W3,D2,L1,V0,M1} { ! distinct_lines( skol3, skol1 )
% 1.19/1.56 }.
% 1.19/1.56 parent0[0]: (27) {G0,W3,D2,L1,V0,M1} I { ! distinct_lines( skol1, skol3 )
% 1.19/1.56 }.
% 1.19/1.56 parent1[1]: (36) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 1.19/1.56 distinct_lines( X, Y ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 end
% 1.19/1.56 substitution1:
% 1.19/1.56 X := skol1
% 1.19/1.56 Y := skol3
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 subsumption: (39) {G2,W3,D2,L1,V0,M1} R(36,27) { ! distinct_lines( skol3,
% 1.19/1.56 skol1 ) }.
% 1.19/1.56 parent0: (4796) {G1,W3,D2,L1,V0,M1} { ! distinct_lines( skol3, skol1 ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 end
% 1.19/1.56 permutation0:
% 1.19/1.56 0 ==> 0
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 resolution: (4797) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 1.19/1.56 convergent_lines( X, Y ) }.
% 1.19/1.56 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 1.19/1.56 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 1.19/1.56 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 X := X
% 1.19/1.56 end
% 1.19/1.56 substitution1:
% 1.19/1.56 X := X
% 1.19/1.56 Y := Y
% 1.19/1.56 Z := X
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 subsumption: (48) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 1.19/1.56 convergent_lines( X, Y ) }.
% 1.19/1.56 parent0: (4797) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 1.19/1.56 convergent_lines( X, Y ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 X := Y
% 1.19/1.56 Y := X
% 1.19/1.56 end
% 1.19/1.56 permutation0:
% 1.19/1.56 0 ==> 1
% 1.19/1.56 1 ==> 0
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 resolution: (4799) {G1,W3,D2,L1,V0,M1} { convergent_lines( skol2, skol3 )
% 1.19/1.56 }.
% 1.19/1.56 parent0[0]: (28) {G0,W3,D2,L1,V0,M1} I { ! unorthogonal_lines( skol2, skol3
% 1.19/1.56 ) }.
% 1.19/1.56 parent1[1]: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 1.19/1.56 unorthogonal_lines( X, Y ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 end
% 1.19/1.56 substitution1:
% 1.19/1.56 X := skol2
% 1.19/1.56 Y := skol3
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 subsumption: (55) {G1,W3,D2,L1,V0,M1} R(17,28) { convergent_lines( skol2,
% 1.19/1.56 skol3 ) }.
% 1.19/1.56 parent0: (4799) {G1,W3,D2,L1,V0,M1} { convergent_lines( skol2, skol3 ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 end
% 1.19/1.56 permutation0:
% 1.19/1.56 0 ==> 0
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 resolution: (4800) {G1,W6,D2,L2,V1,M2} { convergent_lines( skol2, X ),
% 1.19/1.56 convergent_lines( skol3, X ) }.
% 1.19/1.56 parent0[2]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 1.19/1.56 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 1.19/1.56 parent1[0]: (55) {G1,W3,D2,L1,V0,M1} R(17,28) { convergent_lines( skol2,
% 1.19/1.56 skol3 ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 X := skol2
% 1.19/1.56 Y := skol3
% 1.19/1.56 Z := X
% 1.19/1.56 end
% 1.19/1.56 substitution1:
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 subsumption: (57) {G2,W6,D2,L2,V1,M1} R(55,5) { convergent_lines( skol2, X
% 1.19/1.56 ), convergent_lines( skol3, X ) }.
% 1.19/1.56 parent0: (4800) {G1,W6,D2,L2,V1,M2} { convergent_lines( skol2, X ),
% 1.19/1.56 convergent_lines( skol3, X ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 X := X
% 1.19/1.56 end
% 1.19/1.56 permutation0:
% 1.19/1.56 0 ==> 0
% 1.19/1.56 1 ==> 1
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 resolution: (4802) {G2,W6,D2,L2,V1,M2} { convergent_lines( X, skol3 ),
% 1.19/1.56 convergent_lines( skol2, X ) }.
% 1.19/1.56 parent0[0]: (48) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 1.19/1.56 convergent_lines( X, Y ) }.
% 1.19/1.56 parent1[1]: (57) {G2,W6,D2,L2,V1,M1} R(55,5) { convergent_lines( skol2, X )
% 1.19/1.56 , convergent_lines( skol3, X ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 X := X
% 1.19/1.56 Y := skol3
% 1.19/1.56 end
% 1.19/1.56 substitution1:
% 1.19/1.56 X := X
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 subsumption: (61) {G3,W6,D2,L2,V1,M2} R(57,48) { convergent_lines( X, skol3
% 1.19/1.56 ), convergent_lines( skol2, X ) }.
% 1.19/1.56 parent0: (4802) {G2,W6,D2,L2,V1,M2} { convergent_lines( X, skol3 ),
% 1.19/1.56 convergent_lines( skol2, X ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 X := X
% 1.19/1.56 end
% 1.19/1.56 permutation0:
% 1.19/1.56 0 ==> 0
% 1.19/1.56 1 ==> 1
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 resolution: (4803) {G1,W6,D2,L2,V1,M2} { ! convergent_lines( X, skol3 ),
% 1.19/1.56 convergent_lines( X, skol1 ) }.
% 1.19/1.56 parent0[0]: (39) {G2,W3,D2,L1,V0,M1} R(36,27) { ! distinct_lines( skol3,
% 1.19/1.56 skol1 ) }.
% 1.19/1.56 parent1[2]: (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ),
% 1.19/1.56 convergent_lines( X, Z ), distinct_lines( Y, Z ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 end
% 1.19/1.56 substitution1:
% 1.19/1.56 X := X
% 1.19/1.56 Y := skol3
% 1.19/1.56 Z := skol1
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 subsumption: (161) {G3,W6,D2,L2,V1,M1} R(13,39) { convergent_lines( X,
% 1.19/1.56 skol1 ), ! convergent_lines( X, skol3 ) }.
% 1.19/1.56 parent0: (4803) {G1,W6,D2,L2,V1,M2} { ! convergent_lines( X, skol3 ),
% 1.19/1.56 convergent_lines( X, skol1 ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 X := X
% 1.19/1.56 end
% 1.19/1.56 permutation0:
% 1.19/1.56 0 ==> 1
% 1.19/1.56 1 ==> 0
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 resolution: (4805) {G4,W6,D2,L2,V0,M2} { convergent_lines( skol2, skol1 )
% 1.19/1.56 , convergent_lines( skol3, skol3 ) }.
% 1.19/1.56 parent0[1]: (161) {G3,W6,D2,L2,V1,M1} R(13,39) { convergent_lines( X, skol1
% 1.19/1.56 ), ! convergent_lines( X, skol3 ) }.
% 1.19/1.56 parent1[1]: (61) {G3,W6,D2,L2,V1,M2} R(57,48) { convergent_lines( X, skol3
% 1.19/1.56 ), convergent_lines( skol2, X ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 X := skol2
% 1.19/1.56 end
% 1.19/1.56 substitution1:
% 1.19/1.56 X := skol3
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 resolution: (4806) {G1,W3,D2,L1,V0,M1} { convergent_lines( skol2, skol1 )
% 1.19/1.56 }.
% 1.19/1.56 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 1.19/1.56 parent1[1]: (4805) {G4,W6,D2,L2,V0,M2} { convergent_lines( skol2, skol1 )
% 1.19/1.56 , convergent_lines( skol3, skol3 ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 X := skol3
% 1.19/1.56 end
% 1.19/1.56 substitution1:
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 subsumption: (171) {G4,W3,D2,L1,V0,M1} R(161,61);r(2) { convergent_lines(
% 1.19/1.56 skol2, skol1 ) }.
% 1.19/1.56 parent0: (4806) {G1,W3,D2,L1,V0,M1} { convergent_lines( skol2, skol1 ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 end
% 1.19/1.56 permutation0:
% 1.19/1.56 0 ==> 0
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 resolution: (4807) {G2,W6,D2,L2,V1,M2} { convergent_lines( X, skol1 ), !
% 1.19/1.56 convergent_lines( skol3, X ) }.
% 1.19/1.56 parent0[1]: (161) {G3,W6,D2,L2,V1,M1} R(13,39) { convergent_lines( X, skol1
% 1.19/1.56 ), ! convergent_lines( X, skol3 ) }.
% 1.19/1.56 parent1[1]: (48) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 1.19/1.56 convergent_lines( X, Y ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 X := X
% 1.19/1.56 end
% 1.19/1.56 substitution1:
% 1.19/1.56 X := X
% 1.19/1.56 Y := skol3
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 subsumption: (173) {G4,W6,D2,L2,V1,M2} R(161,48) { ! convergent_lines(
% 1.19/1.56 skol3, X ), convergent_lines( X, skol1 ) }.
% 1.19/1.56 parent0: (4807) {G2,W6,D2,L2,V1,M2} { convergent_lines( X, skol1 ), !
% 1.19/1.56 convergent_lines( skol3, X ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 X := X
% 1.19/1.56 end
% 1.19/1.56 permutation0:
% 1.19/1.56 0 ==> 1
% 1.19/1.56 1 ==> 0
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 resolution: (4808) {G2,W3,D2,L1,V0,M1} { convergent_lines( skol1, skol2 )
% 1.19/1.56 }.
% 1.19/1.56 parent0[0]: (48) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 1.19/1.56 convergent_lines( X, Y ) }.
% 1.19/1.56 parent1[0]: (171) {G4,W3,D2,L1,V0,M1} R(161,61);r(2) { convergent_lines(
% 1.19/1.56 skol2, skol1 ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 X := skol1
% 1.19/1.56 Y := skol2
% 1.19/1.56 end
% 1.19/1.56 substitution1:
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 subsumption: (176) {G5,W3,D2,L1,V0,M1} R(171,48) { convergent_lines( skol1
% 1.19/1.56 , skol2 ) }.
% 1.19/1.56 parent0: (4808) {G2,W3,D2,L1,V0,M1} { convergent_lines( skol1, skol2 ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 end
% 1.19/1.56 permutation0:
% 1.19/1.56 0 ==> 0
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 resolution: (4810) {G1,W12,D2,L4,V3,M4} { convergent_lines( X, Y ), !
% 1.19/1.56 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ),
% 1.19/1.56 unorthogonal_lines( Z, Y ) }.
% 1.19/1.56 parent0[1]: (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! alpha1
% 1.19/1.56 ( X, Y ) }.
% 1.19/1.56 parent1[3]: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 1.19/1.56 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 1.19/1.56 }.
% 1.19/1.56 substitution0:
% 1.19/1.56 X := X
% 1.19/1.56 Y := Y
% 1.19/1.56 end
% 1.19/1.56 substitution1:
% 1.19/1.56 X := X
% 1.19/1.56 Y := Z
% 1.19/1.56 Z := Y
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 subsumption: (206) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y
% 1.19/1.56 ), convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 1.19/1.56 unorthogonal_lines( Y, Z ) }.
% 1.19/1.56 parent0: (4810) {G1,W12,D2,L4,V3,M4} { convergent_lines( X, Y ), !
% 1.19/1.56 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ),
% 1.19/1.56 unorthogonal_lines( Z, Y ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 X := X
% 1.19/1.56 Y := Z
% 1.19/1.56 Z := Y
% 1.19/1.56 end
% 1.19/1.56 permutation0:
% 1.19/1.56 0 ==> 1
% 1.19/1.56 1 ==> 0
% 1.19/1.56 2 ==> 2
% 1.19/1.56 3 ==> 3
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 resolution: (4812) {G1,W9,D2,L3,V2,M3} { convergent_lines( X, skol1 ),
% 1.19/1.56 convergent_lines( Y, X ), ! convergent_lines( Y, skol3 ) }.
% 1.19/1.56 parent0[0]: (173) {G4,W6,D2,L2,V1,M2} R(161,48) { ! convergent_lines( skol3
% 1.19/1.56 , X ), convergent_lines( X, skol1 ) }.
% 1.19/1.56 parent1[1]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 1.19/1.56 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 X := X
% 1.19/1.56 end
% 1.19/1.56 substitution1:
% 1.19/1.56 X := Y
% 1.19/1.56 Y := skol3
% 1.19/1.56 Z := X
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 subsumption: (212) {G5,W9,D2,L3,V2,M2} R(173,5) { convergent_lines( X,
% 1.19/1.56 skol1 ), ! convergent_lines( Y, skol3 ), convergent_lines( Y, X ) }.
% 1.19/1.56 parent0: (4812) {G1,W9,D2,L3,V2,M3} { convergent_lines( X, skol1 ),
% 1.19/1.56 convergent_lines( Y, X ), ! convergent_lines( Y, skol3 ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 X := X
% 1.19/1.56 Y := Y
% 1.19/1.56 end
% 1.19/1.56 permutation0:
% 1.19/1.56 0 ==> 0
% 1.19/1.56 1 ==> 2
% 1.19/1.56 2 ==> 1
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 factor: (4815) {G5,W6,D2,L2,V0,M2} { convergent_lines( skol1, skol1 ), !
% 1.19/1.56 convergent_lines( skol1, skol3 ) }.
% 1.19/1.56 parent0[0, 2]: (212) {G5,W9,D2,L3,V2,M2} R(173,5) { convergent_lines( X,
% 1.19/1.56 skol1 ), ! convergent_lines( Y, skol3 ), convergent_lines( Y, X ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 X := skol1
% 1.19/1.56 Y := skol1
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 resolution: (4816) {G1,W3,D2,L1,V0,M1} { ! convergent_lines( skol1, skol3
% 1.19/1.56 ) }.
% 1.19/1.56 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 1.19/1.56 parent1[0]: (4815) {G5,W6,D2,L2,V0,M2} { convergent_lines( skol1, skol1 )
% 1.19/1.56 , ! convergent_lines( skol1, skol3 ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 X := skol1
% 1.19/1.56 end
% 1.19/1.56 substitution1:
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 subsumption: (216) {G6,W3,D2,L1,V0,M1} F(212);r(2) { ! convergent_lines(
% 1.19/1.56 skol1, skol3 ) }.
% 1.19/1.56 parent0: (4816) {G1,W3,D2,L1,V0,M1} { ! convergent_lines( skol1, skol3 )
% 1.19/1.56 }.
% 1.19/1.56 substitution0:
% 1.19/1.56 end
% 1.19/1.56 permutation0:
% 1.19/1.56 0 ==> 0
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 resolution: (4817) {G1,W9,D2,L3,V1,M3} { ! convergent_lines( skol1, skol2
% 1.19/1.56 ), convergent_lines( skol1, X ), unorthogonal_lines( skol2, X ) }.
% 1.19/1.56 parent0[2]: (206) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y
% 1.19/1.56 ), convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 1.19/1.56 unorthogonal_lines( Y, Z ) }.
% 1.19/1.56 parent1[0]: (26) {G0,W3,D2,L1,V0,M1} I { unorthogonal_lines( skol1, skol2 )
% 1.19/1.56 }.
% 1.19/1.56 substitution0:
% 1.19/1.56 X := skol1
% 1.19/1.56 Y := skol2
% 1.19/1.56 Z := X
% 1.19/1.56 end
% 1.19/1.56 substitution1:
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 resolution: (4818) {G2,W6,D2,L2,V1,M2} { convergent_lines( skol1, X ),
% 1.19/1.56 unorthogonal_lines( skol2, X ) }.
% 1.19/1.56 parent0[0]: (4817) {G1,W9,D2,L3,V1,M3} { ! convergent_lines( skol1, skol2
% 1.19/1.56 ), convergent_lines( skol1, X ), unorthogonal_lines( skol2, X ) }.
% 1.19/1.56 parent1[0]: (176) {G5,W3,D2,L1,V0,M1} R(171,48) { convergent_lines( skol1,
% 1.19/1.56 skol2 ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 X := X
% 1.19/1.56 end
% 1.19/1.56 substitution1:
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 subsumption: (4678) {G6,W6,D2,L2,V1,M1} R(206,26);r(176) { convergent_lines
% 1.19/1.56 ( skol1, X ), unorthogonal_lines( skol2, X ) }.
% 1.19/1.56 parent0: (4818) {G2,W6,D2,L2,V1,M2} { convergent_lines( skol1, X ),
% 1.19/1.56 unorthogonal_lines( skol2, X ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 X := X
% 1.19/1.56 end
% 1.19/1.56 permutation0:
% 1.19/1.56 0 ==> 0
% 1.19/1.56 1 ==> 1
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 resolution: (4819) {G1,W3,D2,L1,V0,M1} { convergent_lines( skol1, skol3 )
% 1.19/1.56 }.
% 1.19/1.56 parent0[0]: (28) {G0,W3,D2,L1,V0,M1} I { ! unorthogonal_lines( skol2, skol3
% 1.19/1.56 ) }.
% 1.19/1.56 parent1[1]: (4678) {G6,W6,D2,L2,V1,M1} R(206,26);r(176) { convergent_lines
% 1.19/1.56 ( skol1, X ), unorthogonal_lines( skol2, X ) }.
% 1.19/1.56 substitution0:
% 1.19/1.56 end
% 1.19/1.56 substitution1:
% 1.19/1.56 X := skol3
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 resolution: (4820) {G2,W0,D0,L0,V0,M0} { }.
% 1.19/1.56 parent0[0]: (216) {G6,W3,D2,L1,V0,M1} F(212);r(2) { ! convergent_lines(
% 1.19/1.56 skol1, skol3 ) }.
% 1.19/1.56 parent1[0]: (4819) {G1,W3,D2,L1,V0,M1} { convergent_lines( skol1, skol3 )
% 1.19/1.56 }.
% 1.19/1.56 substitution0:
% 1.19/1.56 end
% 1.19/1.56 substitution1:
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 subsumption: (4683) {G7,W0,D0,L0,V0,M0} R(4678,28);r(216) { }.
% 1.19/1.56 parent0: (4820) {G2,W0,D0,L0,V0,M0} { }.
% 1.19/1.56 substitution0:
% 1.19/1.56 end
% 1.19/1.56 permutation0:
% 1.19/1.56 end
% 1.19/1.56
% 1.19/1.56 Proof check complete!
% 1.19/1.56
% 1.19/1.56 Memory use:
% 1.19/1.56
% 1.19/1.56 space for terms: 61642
% 1.19/1.56 space for clauses: 183681
% 1.19/1.56
% 1.19/1.56
% 1.19/1.56 clauses generated: 45185
% 1.19/1.56 clauses kept: 4684
% 1.19/1.56 clauses selected: 567
% 1.19/1.56 clauses deleted: 0
% 1.19/1.56 clauses inuse deleted: 0
% 1.19/1.56
% 1.19/1.56 subsentry: 815582
% 1.19/1.56 literals s-matched: 252795
% 1.19/1.56 literals matched: 252760
% 1.19/1.56 full subsumption: 142278
% 1.19/1.56
% 1.19/1.56 checksum: 1067422009
% 1.19/1.56
% 1.19/1.56
% 1.19/1.56 Bliksem ended
%------------------------------------------------------------------------------