TSTP Solution File: GEO196+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO196+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Sat Jul 16 02:52:35 EDT 2022
% Result : Theorem 51.95s 52.37s
% Output : Refutation 51.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO196+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Fri Jun 17 18:04:02 EDT 2022
% 0.13/0.34 % CPUTime :
% 51.95/52.37 *** allocated 10000 integers for termspace/termends
% 51.95/52.37 *** allocated 10000 integers for clauses
% 51.95/52.37 *** allocated 10000 integers for justifications
% 51.95/52.37 Bliksem 1.12
% 51.95/52.37
% 51.95/52.37
% 51.95/52.37 Automatic Strategy Selection
% 51.95/52.37
% 51.95/52.37
% 51.95/52.37 Clauses:
% 51.95/52.37
% 51.95/52.37 { ! distinct_points( X, X ) }.
% 51.95/52.37 { ! distinct_lines( X, X ) }.
% 51.95/52.37 { ! convergent_lines( X, X ) }.
% 51.95/52.37 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 51.95/52.37 ) }.
% 51.95/52.37 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 51.95/52.37 }.
% 51.95/52.37 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 51.95/52.37 , Z ) }.
% 51.95/52.37 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 51.95/52.37 , Y ) ) }.
% 51.95/52.37 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 51.95/52.37 , Y ) ) }.
% 51.95/52.37 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 51.95/52.37 , Y ), X ) }.
% 51.95/52.37 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 51.95/52.37 , Y ), Y ) }.
% 51.95/52.37 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 51.95/52.37 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 51.95/52.37 apart_point_and_line( Y, T ) }.
% 51.95/52.37 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 51.95/52.37 apart_point_and_line( Z, Y ) }.
% 51.95/52.37 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 51.95/52.37 apart_point_and_line( X, Z ) }.
% 51.95/52.37 { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X,
% 51.95/52.37 Z ) }.
% 51.95/52.37 { convergent_lines( skol1, skol2 ) }.
% 51.95/52.37 { convergent_lines( skol3, skol4 ) }.
% 51.95/52.37 { ! apart_point_and_line( intersection_point( skol1, skol2 ), skol3 ) }.
% 51.95/52.37 { ! apart_point_and_line( intersection_point( skol1, skol2 ), skol4 ) }.
% 51.95/52.37 { apart_point_and_line( intersection_point( skol3, skol4 ), skol1 ),
% 51.95/52.37 apart_point_and_line( intersection_point( skol3, skol4 ), skol2 ) }.
% 51.95/52.37
% 51.95/52.37 percentage equality = 0.000000, percentage horn = 0.578947
% 51.95/52.37 This a non-horn, non-equality problem
% 51.95/52.37
% 51.95/52.37
% 51.95/52.37 Options Used:
% 51.95/52.37
% 51.95/52.37 useres = 1
% 51.95/52.37 useparamod = 0
% 51.95/52.37 useeqrefl = 0
% 51.95/52.37 useeqfact = 0
% 51.95/52.37 usefactor = 1
% 51.95/52.37 usesimpsplitting = 0
% 51.95/52.37 usesimpdemod = 0
% 51.95/52.37 usesimpres = 3
% 51.95/52.37
% 51.95/52.37 resimpinuse = 1000
% 51.95/52.37 resimpclauses = 20000
% 51.95/52.37 substype = standard
% 51.95/52.37 backwardsubs = 1
% 51.95/52.37 selectoldest = 5
% 51.95/52.37
% 51.95/52.37 litorderings [0] = split
% 51.95/52.37 litorderings [1] = liftord
% 51.95/52.37
% 51.95/52.37 termordering = none
% 51.95/52.37
% 51.95/52.37 litapriori = 1
% 51.95/52.37 termapriori = 0
% 51.95/52.37 litaposteriori = 0
% 51.95/52.37 termaposteriori = 0
% 51.95/52.37 demodaposteriori = 0
% 51.95/52.37 ordereqreflfact = 0
% 51.95/52.37
% 51.95/52.37 litselect = none
% 51.95/52.37
% 51.95/52.37 maxweight = 15
% 51.95/52.37 maxdepth = 30000
% 51.95/52.37 maxlength = 115
% 51.95/52.37 maxnrvars = 195
% 51.95/52.37 excuselevel = 1
% 51.95/52.37 increasemaxweight = 1
% 51.95/52.37
% 51.95/52.37 maxselected = 10000000
% 51.95/52.37 maxnrclauses = 10000000
% 51.95/52.37
% 51.95/52.37 showgenerated = 0
% 51.95/52.37 showkept = 0
% 51.95/52.37 showselected = 0
% 51.95/52.37 showdeleted = 0
% 51.95/52.37 showresimp = 1
% 51.95/52.37 showstatus = 2000
% 51.95/52.37
% 51.95/52.37 prologoutput = 0
% 51.95/52.37 nrgoals = 5000000
% 51.95/52.37 totalproof = 1
% 51.95/52.37
% 51.95/52.37 Symbols occurring in the translation:
% 51.95/52.37
% 51.95/52.37 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 51.95/52.37 . [1, 2] (w:1, o:20, a:1, s:1, b:0),
% 51.95/52.37 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 51.95/52.37 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 51.95/52.37 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 51.95/52.37 distinct_points [36, 2] (w:1, o:45, a:1, s:1, b:0),
% 51.95/52.37 distinct_lines [37, 2] (w:1, o:46, a:1, s:1, b:0),
% 51.95/52.37 convergent_lines [38, 2] (w:1, o:44, a:1, s:1, b:0),
% 51.95/52.37 line_connecting [41, 2] (w:1, o:47, a:1, s:1, b:0),
% 51.95/52.37 apart_point_and_line [42, 2] (w:1, o:48, a:1, s:1, b:0),
% 51.95/52.37 intersection_point [43, 2] (w:1, o:49, a:1, s:1, b:0),
% 51.95/52.37 skol1 [46, 0] (w:1, o:11, a:1, s:1, b:0),
% 51.95/52.37 skol2 [47, 0] (w:1, o:12, a:1, s:1, b:0),
% 51.95/52.37 skol3 [48, 0] (w:1, o:13, a:1, s:1, b:0),
% 51.95/52.37 skol4 [49, 0] (w:1, o:14, a:1, s:1, b:0).
% 51.95/52.37
% 51.95/52.37
% 51.95/52.37 Starting Search:
% 51.95/52.37
% 51.95/52.37 *** allocated 15000 integers for clauses
% 51.95/52.37 *** allocated 22500 integers for clauses
% 51.95/52.37 *** allocated 33750 integers for clauses
% 51.95/52.37 *** allocated 15000 integers for termspace/termends
% 51.95/52.37 *** allocated 50625 integers for clauses
% 51.95/52.37 Resimplifying inuse:
% 51.95/52.37 Done
% 51.95/52.37
% 51.95/52.37 *** allocated 22500 integers for termspace/termends
% 51.95/52.37 *** allocated 75937 integers for clauses
% 51.95/52.37 *** allocated 33750 integers for termspace/termends
% 51.95/52.37
% 51.95/52.37 Intermediate Status:
% 51.95/52.37 Generated: 21715
% 51.95/52.37 Kept: 2078
% 51.95/52.37 Inuse: 361
% 51.95/52.37 Deleted: 0
% 51.95/52.37 Deletedinuse: 0
% 51.95/52.37
% 51.95/52.37 Resimplifying inuse:
% 51.95/52.37 Done
% 51.95/52.37
% 51.95/52.37 *** allocated 113905 integers for clauses
% 51.95/52.37 *** allocated 50625 integers for termspace/termends
% 51.95/52.37 Resimplifying inuse:
% 51.95/52.37 Done
% 51.95/52.37
% 51.95/52.37 Failed to find proof!
% 51.95/52.37 maxweight = 15
% 51.95/52.37 maxnrclauses = 10000000
% 51.95/52.37 Generated: 353998
% 51.95/52.37 Kept: 2957
% 51.95/52.37
% 51.95/52.37
% 51.95/52.37 The strategy used was not complete!
% 51.95/52.37
% 51.95/52.37 Increased maxweight to 16
% 51.95/52.37
% 51.95/52.37 Starting Search:
% 51.95/52.37
% 51.95/52.37 Resimplifying inuse:
% 51.95/52.37 Done
% 51.95/52.37
% 51.95/52.37
% 51.95/52.37 Intermediate Status:
% 51.95/52.37 Generated: 19956
% 51.95/52.37 Kept: 2003
% 51.95/52.37 Inuse: 359
% 51.95/52.37 Deleted: 0
% 51.95/52.37 Deletedinuse: 0
% 51.95/52.37
% 51.95/52.37 Resimplifying inuse:
% 51.95/52.37 Done
% 51.95/52.37
% 51.95/52.37 Resimplifying inuse:
% 51.95/52.37 Done
% 51.95/52.37
% 51.95/52.37 *** allocated 170857 integers for clauses
% 51.95/52.37 Resimplifying inuse:
% 51.95/52.37 Done
% 51.95/52.37
% 51.95/52.37 Failed to find proof!
% 51.95/52.37 maxweight = 16
% 51.95/52.37 maxnrclauses = 10000000
% 51.95/52.37 Generated: 389108
% 51.95/52.37 Kept: 3453
% 51.95/52.37
% 51.95/52.37
% 51.95/52.37 The strategy used was not complete!
% 51.95/52.37
% 51.95/52.37 Increased maxweight to 17
% 51.95/52.37
% 51.95/52.37 Starting Search:
% 51.95/52.37
% 51.95/52.37 Resimplifying inuse:
% 51.95/52.37 Done
% 51.95/52.37
% 51.95/52.37
% 51.95/52.37 Intermediate Status:
% 51.95/52.37 Generated: 19797
% 51.95/52.37 Kept: 2118
% 51.95/52.37 Inuse: 346
% 51.95/52.37 Deleted: 0
% 51.95/52.37 Deletedinuse: 0
% 51.95/52.37
% 51.95/52.37 Resimplifying inuse:
% 51.95/52.37 Done
% 51.95/52.37
% 51.95/52.37 Resimplifying inuse:
% 51.95/52.37 Done
% 51.95/52.37
% 51.95/52.37 *** allocated 75937 integers for termspace/termends
% 51.95/52.37
% 51.95/52.37 Intermediate Status:
% 51.95/52.37 Generated: 40151
% 51.95/52.37 Kept: 4121
% 51.95/52.37 Inuse: 502
% 51.95/52.37 Deleted: 0
% 51.95/52.37 Deletedinuse: 0
% 51.95/52.37
% 51.95/52.37 Resimplifying inuse:
% 51.95/52.37 Done
% 51.95/52.37
% 51.95/52.37 Resimplifying inuse:
% 51.95/52.37 Done
% 51.95/52.37
% 51.95/52.37 Failed to find proof!
% 51.95/52.37 maxweight = 17
% 51.95/52.37 maxnrclauses = 10000000
% 51.95/52.37 Generated: 1087608
% 51.95/52.37 Kept: 4805
% 51.95/52.37
% 51.95/52.37
% 51.95/52.37 The strategy used was not complete!
% 51.95/52.37
% 51.95/52.37 Increased maxweight to 18
% 51.95/52.37
% 51.95/52.37 Starting Search:
% 51.95/52.37
% 51.95/52.37 Resimplifying inuse:
% 51.95/52.37 Done
% 51.95/52.37
% 51.95/52.37
% 51.95/52.37 Intermediate Status:
% 51.95/52.37 Generated: 20435
% 51.95/52.37 Kept: 2226
% 51.95/52.37 Inuse: 346
% 51.95/52.37 Deleted: 0
% 51.95/52.37 Deletedinuse: 0
% 51.95/52.37
% 51.95/52.37 Resimplifying inuse:
% 51.95/52.37 Done
% 51.95/52.37
% 51.95/52.37 Resimplifying inuse:
% 51.95/52.37 Done
% 51.95/52.37
% 51.95/52.37
% 51.95/52.37 Intermediate Status:
% 51.95/52.37 Generated: 33548
% 51.95/52.37 Kept: 4261
% 51.95/52.37 Inuse: 432
% 51.95/52.37 Deleted: 0
% 51.95/52.37 Deletedinuse: 0
% 51.95/52.37
% 51.95/52.37 Resimplifying inuse:
% 51.95/52.37 Done
% 51.95/52.37
% 51.95/52.37 *** allocated 113905 integers for termspace/termends
% 51.95/52.37 *** allocated 256285 integers for clauses
% 51.95/52.37 Resimplifying inuse:
% 51.95/52.37 Done
% 51.95/52.37
% 51.95/52.37
% 51.95/52.37 Intermediate Status:
% 51.95/52.37 Generated: 69710
% 51.95/52.37 Kept: 6268
% 51.95/52.37 Inuse: 561
% 51.95/52.37 Deleted: 0
% 51.95/52.37 Deletedinuse: 0
% 51.95/52.37
% 51.95/52.37 Resimplifying inuse:
% 51.95/52.37 Done
% 51.95/52.37
% 51.95/52.37 *** allocated 170857 integers for termspace/termends
% 51.95/52.37 Resimplifying inuse:
% 51.95/52.37 Done
% 51.95/52.37
% 51.95/52.37 *** allocated 384427 integers for clauses
% 51.95/52.37
% 51.95/52.37 Intermediate Status:
% 51.95/52.37 Generated: 150599
% 51.95/52.37 Kept: 8279
% 51.95/52.37 Inuse: 964
% 51.95/52.37 Deleted: 4
% 51.95/52.37 Deletedinuse: 0
% 51.95/52.37
% 51.95/52.37 Resimplifying inuse:
% 51.95/52.37 Done
% 51.95/52.37
% 51.95/52.37 Resimplifying inuse:
% 51.95/52.37 Done
% 51.95/52.37
% 51.95/52.37 *** allocated 256285 integers for termspace/termends
% 51.95/52.37
% 51.95/52.37 Intermediate Status:
% 51.95/52.37 Generated: 1922545
% 51.95/52.37 Kept: 10279
% 51.95/52.37 Inuse: 5663
% 51.95/52.37 Deleted: 63
% 51.95/52.37 Deletedinuse: 0
% 51.95/52.37
% 51.95/52.37 Resimplifying inuse:
% 51.95/52.37 Done
% 51.95/52.37
% 51.95/52.37
% 51.95/52.37 Bliksems!, er is een bewijs:
% 51.95/52.37 % SZS status Theorem
% 51.95/52.37 % SZS output start Refutation
% 51.95/52.37
% 51.95/52.37 (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 51.95/52.37 (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 51.95/52.37 (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 51.95/52.37 , ! distinct_lines( X, Y ) }.
% 51.95/52.37 (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), convergent_lines( Y,
% 51.95/52.37 Z ), ! convergent_lines( X, Y ) }.
% 51.95/52.37 (8) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 51.95/52.37 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 51.95/52.37 (9) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 51.95/52.37 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 51.95/52.37 (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! distinct_lines(
% 51.95/52.37 Z, T ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 51.95/52.37 apart_point_and_line( Y, T ), apart_point_and_line( X, Z ) }.
% 51.95/52.37 (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), apart_point_and_line
% 51.95/52.37 ( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 51.95/52.37 (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ), convergent_lines(
% 51.95/52.37 X, Z ), distinct_lines( Y, Z ) }.
% 51.95/52.37 (14) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 ) }.
% 51.95/52.37 (15) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol3, skol4 ) }.
% 51.95/52.37 (16) {G0,W5,D3,L1,V0,M1} I { ! apart_point_and_line( intersection_point(
% 51.95/52.37 skol1, skol2 ), skol3 ) }.
% 51.95/52.37 (17) {G0,W5,D3,L1,V0,M1} I { ! apart_point_and_line( intersection_point(
% 51.95/52.37 skol1, skol2 ), skol4 ) }.
% 51.95/52.37 (18) {G0,W10,D3,L2,V0,M1} I { apart_point_and_line( intersection_point(
% 51.95/52.37 skol3, skol4 ), skol1 ), apart_point_and_line( intersection_point( skol3
% 51.95/52.37 , skol4 ), skol2 ) }.
% 51.95/52.37 (26) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 51.95/52.37 ( X, Y ) }.
% 51.95/52.37 (32) {G1,W6,D2,L2,V1,M1} R(5,15) { convergent_lines( skol3, X ),
% 51.95/52.37 convergent_lines( skol4, X ) }.
% 51.95/52.37 (33) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 51.95/52.37 convergent_lines( X, Y ) }.
% 51.95/52.37 (48) {G1,W22,D3,L6,V4,M3} R(10,8) { ! distinct_points( intersection_point(
% 51.95/52.37 X, Y ), Z ), ! distinct_lines( T, X ), ! convergent_lines( X, Y ),
% 51.95/52.37 apart_point_and_line( intersection_point( X, Y ), T ),
% 51.95/52.37 apart_point_and_line( Z, T ), apart_point_and_line( Z, X ) }.
% 51.95/52.37 (71) {G2,W6,D2,L2,V1,M2} R(32,33) { convergent_lines( X, skol4 ),
% 51.95/52.37 convergent_lines( skol3, X ) }.
% 51.95/52.37 (81) {G1,W11,D3,L3,V3,M1} R(11,9) { distinct_points( X, intersection_point
% 51.95/52.37 ( Y, Z ) ), ! convergent_lines( Y, Z ), ! apart_point_and_line( X, Z )
% 51.95/52.37 }.
% 51.95/52.37 (84) {G3,W6,D2,L2,V1,M1} R(71,33) { convergent_lines( X, skol3 ),
% 51.95/52.37 convergent_lines( X, skol4 ) }.
% 51.95/52.37 (120) {G2,W9,D2,L3,V3,M1} R(13,26) { ! convergent_lines( X, Y ),
% 51.95/52.37 convergent_lines( X, Z ), distinct_lines( Z, Y ) }.
% 51.95/52.37 (572) {G2,W17,D3,L5,V3,M2} R(48,9);f { ! distinct_points(
% 51.95/52.37 intersection_point( X, Y ), Z ), ! convergent_lines( X, Y ), !
% 51.95/52.37 distinct_lines( Y, X ), apart_point_and_line( Z, X ),
% 51.95/52.37 apart_point_and_line( Z, Y ) }.
% 51.95/52.37 (1307) {G2,W15,D3,L3,V1,M1} R(81,18) { ! convergent_lines( X, skol2 ),
% 51.95/52.37 distinct_points( intersection_point( skol3, skol4 ), intersection_point(
% 51.95/52.37 X, skol2 ) ), apart_point_and_line( intersection_point( skol3, skol4 ),
% 51.95/52.37 skol1 ) }.
% 51.95/52.37 (8945) {G3,W18,D3,L4,V1,M1} R(572,16) { ! convergent_lines( skol3, X ), !
% 51.95/52.37 distinct_points( intersection_point( skol3, X ), intersection_point(
% 51.95/52.37 skol1, skol2 ) ), ! distinct_lines( X, skol3 ), apart_point_and_line(
% 51.95/52.37 intersection_point( skol1, skol2 ), X ) }.
% 51.95/52.37 (9733) {G3,W18,D3,L4,V2,M1} R(1307,11) { ! convergent_lines( X, skol2 ),
% 51.95/52.37 distinct_points( intersection_point( skol3, skol4 ), intersection_point(
% 51.95/52.37 X, skol2 ) ), distinct_points( intersection_point( skol3, skol4 ), Y ),
% 51.95/52.37 apart_point_and_line( Y, skol1 ) }.
% 51.95/52.37 (9734) {G4,W15,D3,L3,V1,M1} F(9733) { ! convergent_lines( X, skol2 ),
% 51.95/52.37 distinct_points( intersection_point( skol3, skol4 ), intersection_point(
% 51.95/52.37 X, skol2 ) ), apart_point_and_line( intersection_point( X, skol2 ), skol1
% 51.95/52.37 ) }.
% 51.95/52.37 (9787) {G5,W7,D3,L1,V0,M1} R(9734,8);f;r(14) { distinct_points(
% 51.95/52.37 intersection_point( skol3, skol4 ), intersection_point( skol1, skol2 ) )
% 51.95/52.37 }.
% 51.95/52.37 (10466) {G4,W10,D3,L2,V0,M1} R(8945,17);r(15) { ! distinct_points(
% 51.95/52.37 intersection_point( skol3, skol4 ), intersection_point( skol1, skol2 ) )
% 51.95/52.37 , ! distinct_lines( skol4, skol3 ) }.
% 51.95/52.37 (10467) {G6,W3,D2,L1,V0,M1} S(10466);r(9787) { ! distinct_lines( skol4,
% 51.95/52.37 skol3 ) }.
% 51.95/52.37 (10834) {G7,W3,D2,L1,V1,M1} R(10467,120);r(84) { convergent_lines( X, skol4
% 51.95/52.37 ) }.
% 51.95/52.37 (10875) {G8,W0,D0,L0,V0,M0} R(10834,2) { }.
% 51.95/52.37
% 51.95/52.37
% 51.95/52.37 % SZS output end Refutation
% 51.95/52.37 found a proof!
% 51.95/52.37
% 51.95/52.37
% 51.95/52.37 Unprocessed initial clauses:
% 51.95/52.37
% 51.95/52.37 (10877) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 51.95/52.37 (10878) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 51.95/52.37 (10879) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 51.95/52.37 (10880) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points(
% 51.95/52.37 X, Z ), distinct_points( Y, Z ) }.
% 51.95/52.37 (10881) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X
% 51.95/52.37 , Z ), distinct_lines( Y, Z ) }.
% 51.95/52.37 (10882) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines
% 51.95/52.37 ( X, Z ), convergent_lines( Y, Z ) }.
% 51.95/52.37 (10883) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 51.95/52.37 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 51.95/52.37 (10884) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 51.95/52.37 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 51.95/52.37 (10885) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 51.95/52.37 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 51.95/52.37 (10886) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 51.95/52.37 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 51.95/52.37 (10887) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines
% 51.95/52.37 ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 51.95/52.37 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 51.95/52.37 (10888) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 51.95/52.37 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 51.95/52.37 (10889) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 51.95/52.37 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 51.95/52.37 (10890) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), distinct_lines(
% 51.95/52.37 Y, Z ), convergent_lines( X, Z ) }.
% 51.95/52.37 (10891) {G0,W3,D2,L1,V0,M1} { convergent_lines( skol1, skol2 ) }.
% 51.95/52.37 (10892) {G0,W3,D2,L1,V0,M1} { convergent_lines( skol3, skol4 ) }.
% 51.95/52.37 (10893) {G0,W5,D3,L1,V0,M1} { ! apart_point_and_line( intersection_point(
% 51.95/52.37 skol1, skol2 ), skol3 ) }.
% 51.95/52.37 (10894) {G0,W5,D3,L1,V0,M1} { ! apart_point_and_line( intersection_point(
% 51.95/52.37 skol1, skol2 ), skol4 ) }.
% 51.95/52.37 (10895) {G0,W10,D3,L2,V0,M2} { apart_point_and_line( intersection_point(
% 51.95/52.37 skol3, skol4 ), skol1 ), apart_point_and_line( intersection_point( skol3
% 51.95/52.37 , skol4 ), skol2 ) }.
% 51.95/52.37
% 51.95/52.37
% 51.95/52.37 Total Proof:
% 51.95/52.37
% 51.95/52.37 subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 51.95/52.37 parent0: (10878) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 51.95/52.37 substitution0:
% 51.95/52.37 X := X
% 51.95/52.37 end
% 51.95/52.37 permutation0:
% 51.95/52.37 0 ==> 0
% 51.95/52.37 end
% 51.95/52.37
% 51.95/52.37 subsumption: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 51.95/52.37 parent0: (10879) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 51.95/52.37 substitution0:
% 51.95/52.37 X := X
% 51.95/52.37 end
% 51.95/52.37 permutation0:
% 51.95/52.37 0 ==> 0
% 51.95/52.37 end
% 51.95/52.37
% 51.95/52.37 subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 51.95/52.37 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 51.95/52.37 parent0: (10881) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ),
% 51.95/52.37 distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 51.95/52.37 substitution0:
% 51.95/52.37 X := X
% 51.95/52.37 Y := Y
% 51.95/52.37 Z := Z
% 51.95/52.37 end
% 51.95/52.37 permutation0:
% 51.95/52.37 0 ==> 2
% 51.95/52.37 1 ==> 0
% 51.95/52.37 2 ==> 1
% 51.95/52.37 end
% 51.95/52.37
% 51.95/52.37 subsumption: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 51.95/52.37 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 51.95/52.37 parent0: (10882) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 51.95/52.37 convergent_lines( X, Z ), convergent_lines( Y, Z ) }.
% 51.95/52.37 substitution0:
% 51.95/52.37 X := X
% 51.95/52.37 Y := Y
% 51.95/52.37 Z := Z
% 51.95/52.37 end
% 51.95/52.37 permutation0:
% 51.95/52.37 0 ==> 2
% 51.95/52.37 1 ==> 0
% 51.95/52.37 2 ==> 1
% 51.95/52.37 end
% 51.95/52.37
% 51.95/52.37 subsumption: (8) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 51.95/52.37 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 51.95/52.37 parent0: (10885) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 51.95/52.37 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 51.95/52.37 substitution0:
% 51.95/52.37 X := X
% 51.95/52.37 Y := Y
% 51.95/52.37 end
% 51.95/52.37 permutation0:
% 51.95/52.37 0 ==> 0
% 51.95/52.37 1 ==> 1
% 51.95/52.37 end
% 51.95/52.37
% 51.95/52.37 subsumption: (9) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 51.95/52.37 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 51.95/52.37 parent0: (10886) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 51.95/52.37 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 51.95/52.37 substitution0:
% 51.95/52.37 X := X
% 51.95/52.37 Y := Y
% 51.95/52.37 end
% 51.95/52.37 permutation0:
% 51.95/52.37 0 ==> 0
% 51.95/52.37 1 ==> 1
% 51.95/52.37 end
% 51.95/52.37
% 51.95/52.37 subsumption: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), !
% 51.95/52.37 distinct_lines( Z, T ), apart_point_and_line( X, T ),
% 51.95/52.37 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ),
% 51.95/52.37 apart_point_and_line( X, Z ) }.
% 51.95/52.37 parent0: (10887) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), !
% 51.95/52.37 distinct_lines( Z, T ), apart_point_and_line( X, Z ),
% 51.95/52.37 apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 51.95/52.37 apart_point_and_line( Y, T ) }.
% 51.95/52.37 substitution0:
% 51.95/52.37 X := X
% 51.95/52.37 Y := Y
% 51.95/52.37 Z := Z
% 51.95/52.37 T := T
% 51.95/52.37 end
% 51.95/52.37 permutation0:
% 51.95/52.37 0 ==> 0
% 51.95/52.37 1 ==> 1
% 51.95/52.37 2 ==> 5
% 51.95/52.37 3 ==> 2
% 51.95/52.37 4 ==> 3
% 51.95/52.37 5 ==> 4
% 51.95/52.37 end
% 51.95/52.37
% 51.95/52.37 subsumption: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ),
% 51.95/52.37 apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 51.95/52.37 parent0: (10888) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 51.95/52.37 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 51.95/52.37 substitution0:
% 51.95/52.37 X := X
% 51.95/52.37 Y := Y
% 51.95/52.37 Z := Z
% 51.95/52.37 end
% 51.95/52.37 permutation0:
% 51.95/52.37 0 ==> 2
% 51.95/52.37 1 ==> 0
% 51.95/52.37 2 ==> 1
% 51.95/52.37 end
% 51.95/52.37
% 51.95/52.37 subsumption: (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ),
% 51.95/52.37 convergent_lines( X, Z ), distinct_lines( Y, Z ) }.
% 51.95/52.37 parent0: (10890) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 51.95/52.37 distinct_lines( Y, Z ), convergent_lines( X, Z ) }.
% 51.95/52.37 substitution0:
% 51.95/52.37 X := X
% 51.95/52.37 Y := Y
% 51.95/52.37 Z := Z
% 51.95/52.37 end
% 51.95/52.37 permutation0:
% 51.95/52.37 0 ==> 0
% 51.95/52.37 1 ==> 2
% 51.95/52.37 2 ==> 1
% 51.95/52.37 end
% 51.95/52.37
% 51.95/52.37 subsumption: (14) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 )
% 51.95/52.37 }.
% 51.95/52.37 parent0: (10891) {G0,W3,D2,L1,V0,M1} { convergent_lines( skol1, skol2 )
% 51.95/52.37 }.
% 51.95/52.37 substitution0:
% 51.95/52.37 end
% 51.95/52.37 permutation0:
% 51.95/52.37 0 ==> 0
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 subsumption: (15) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol3, skol4 )
% 51.95/52.38 }.
% 51.95/52.38 parent0: (10892) {G0,W3,D2,L1,V0,M1} { convergent_lines( skol3, skol4 )
% 51.95/52.38 }.
% 51.95/52.38 substitution0:
% 51.95/52.38 end
% 51.95/52.38 permutation0:
% 51.95/52.38 0 ==> 0
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 subsumption: (16) {G0,W5,D3,L1,V0,M1} I { ! apart_point_and_line(
% 51.95/52.38 intersection_point( skol1, skol2 ), skol3 ) }.
% 51.95/52.38 parent0: (10893) {G0,W5,D3,L1,V0,M1} { ! apart_point_and_line(
% 51.95/52.38 intersection_point( skol1, skol2 ), skol3 ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 end
% 51.95/52.38 permutation0:
% 51.95/52.38 0 ==> 0
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 subsumption: (17) {G0,W5,D3,L1,V0,M1} I { ! apart_point_and_line(
% 51.95/52.38 intersection_point( skol1, skol2 ), skol4 ) }.
% 51.95/52.38 parent0: (10894) {G0,W5,D3,L1,V0,M1} { ! apart_point_and_line(
% 51.95/52.38 intersection_point( skol1, skol2 ), skol4 ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 end
% 51.95/52.38 permutation0:
% 51.95/52.38 0 ==> 0
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 subsumption: (18) {G0,W10,D3,L2,V0,M1} I { apart_point_and_line(
% 51.95/52.38 intersection_point( skol3, skol4 ), skol1 ), apart_point_and_line(
% 51.95/52.38 intersection_point( skol3, skol4 ), skol2 ) }.
% 51.95/52.38 parent0: (10895) {G0,W10,D3,L2,V0,M2} { apart_point_and_line(
% 51.95/52.38 intersection_point( skol3, skol4 ), skol1 ), apart_point_and_line(
% 51.95/52.38 intersection_point( skol3, skol4 ), skol2 ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 end
% 51.95/52.38 permutation0:
% 51.95/52.38 0 ==> 0
% 51.95/52.38 1 ==> 1
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 resolution: (10979) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 51.95/52.38 distinct_lines( X, Y ) }.
% 51.95/52.38 parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 51.95/52.38 parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 51.95/52.38 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 X := X
% 51.95/52.38 end
% 51.95/52.38 substitution1:
% 51.95/52.38 X := X
% 51.95/52.38 Y := Y
% 51.95/52.38 Z := X
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 subsumption: (26) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 51.95/52.38 distinct_lines( X, Y ) }.
% 51.95/52.38 parent0: (10979) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 51.95/52.38 distinct_lines( X, Y ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 X := Y
% 51.95/52.38 Y := X
% 51.95/52.38 end
% 51.95/52.38 permutation0:
% 51.95/52.38 0 ==> 1
% 51.95/52.38 1 ==> 0
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 resolution: (10981) {G1,W6,D2,L2,V1,M2} { convergent_lines( skol3, X ),
% 51.95/52.38 convergent_lines( skol4, X ) }.
% 51.95/52.38 parent0[2]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 51.95/52.38 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 51.95/52.38 parent1[0]: (15) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol3, skol4 )
% 51.95/52.38 }.
% 51.95/52.38 substitution0:
% 51.95/52.38 X := skol3
% 51.95/52.38 Y := skol4
% 51.95/52.38 Z := X
% 51.95/52.38 end
% 51.95/52.38 substitution1:
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 subsumption: (32) {G1,W6,D2,L2,V1,M1} R(5,15) { convergent_lines( skol3, X
% 51.95/52.38 ), convergent_lines( skol4, X ) }.
% 51.95/52.38 parent0: (10981) {G1,W6,D2,L2,V1,M2} { convergent_lines( skol3, X ),
% 51.95/52.38 convergent_lines( skol4, X ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 X := X
% 51.95/52.38 end
% 51.95/52.38 permutation0:
% 51.95/52.38 0 ==> 0
% 51.95/52.38 1 ==> 1
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 resolution: (10982) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 51.95/52.38 convergent_lines( X, Y ) }.
% 51.95/52.38 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 51.95/52.38 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 51.95/52.38 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 X := X
% 51.95/52.38 end
% 51.95/52.38 substitution1:
% 51.95/52.38 X := X
% 51.95/52.38 Y := Y
% 51.95/52.38 Z := X
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 subsumption: (33) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 51.95/52.38 convergent_lines( X, Y ) }.
% 51.95/52.38 parent0: (10982) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 51.95/52.38 convergent_lines( X, Y ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 X := Y
% 51.95/52.38 Y := X
% 51.95/52.38 end
% 51.95/52.38 permutation0:
% 51.95/52.38 0 ==> 1
% 51.95/52.38 1 ==> 0
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 resolution: (10984) {G1,W22,D3,L6,V4,M6} { ! convergent_lines( X, Y ), !
% 51.95/52.38 distinct_points( intersection_point( X, Y ), Z ), ! distinct_lines( T, X
% 51.95/52.38 ), apart_point_and_line( Z, T ), apart_point_and_line( Z, X ),
% 51.95/52.38 apart_point_and_line( intersection_point( X, Y ), T ) }.
% 51.95/52.38 parent0[1]: (8) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 51.95/52.38 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 51.95/52.38 parent1[2]: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), !
% 51.95/52.38 distinct_lines( Z, T ), apart_point_and_line( X, T ),
% 51.95/52.38 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ),
% 51.95/52.38 apart_point_and_line( X, Z ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 X := X
% 51.95/52.38 Y := Y
% 51.95/52.38 end
% 51.95/52.38 substitution1:
% 51.95/52.38 X := intersection_point( X, Y )
% 51.95/52.38 Y := Z
% 51.95/52.38 Z := T
% 51.95/52.38 T := X
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 subsumption: (48) {G1,W22,D3,L6,V4,M3} R(10,8) { ! distinct_points(
% 51.95/52.38 intersection_point( X, Y ), Z ), ! distinct_lines( T, X ), !
% 51.95/52.38 convergent_lines( X, Y ), apart_point_and_line( intersection_point( X, Y
% 51.95/52.38 ), T ), apart_point_and_line( Z, T ), apart_point_and_line( Z, X ) }.
% 51.95/52.38 parent0: (10984) {G1,W22,D3,L6,V4,M6} { ! convergent_lines( X, Y ), !
% 51.95/52.38 distinct_points( intersection_point( X, Y ), Z ), ! distinct_lines( T, X
% 51.95/52.38 ), apart_point_and_line( Z, T ), apart_point_and_line( Z, X ),
% 51.95/52.38 apart_point_and_line( intersection_point( X, Y ), T ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 X := X
% 51.95/52.38 Y := Y
% 51.95/52.38 Z := Z
% 51.95/52.38 T := T
% 51.95/52.38 end
% 51.95/52.38 permutation0:
% 51.95/52.38 0 ==> 2
% 51.95/52.38 1 ==> 0
% 51.95/52.38 2 ==> 1
% 51.95/52.38 3 ==> 4
% 51.95/52.38 4 ==> 5
% 51.95/52.38 5 ==> 3
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 resolution: (10994) {G2,W6,D2,L2,V1,M2} { convergent_lines( X, skol4 ),
% 51.95/52.38 convergent_lines( skol3, X ) }.
% 51.95/52.38 parent0[0]: (33) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 51.95/52.38 convergent_lines( X, Y ) }.
% 51.95/52.38 parent1[1]: (32) {G1,W6,D2,L2,V1,M1} R(5,15) { convergent_lines( skol3, X )
% 51.95/52.38 , convergent_lines( skol4, X ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 X := X
% 51.95/52.38 Y := skol4
% 51.95/52.38 end
% 51.95/52.38 substitution1:
% 51.95/52.38 X := X
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 subsumption: (71) {G2,W6,D2,L2,V1,M2} R(32,33) { convergent_lines( X, skol4
% 51.95/52.38 ), convergent_lines( skol3, X ) }.
% 51.95/52.38 parent0: (10994) {G2,W6,D2,L2,V1,M2} { convergent_lines( X, skol4 ),
% 51.95/52.38 convergent_lines( skol3, X ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 X := X
% 51.95/52.38 end
% 51.95/52.38 permutation0:
% 51.95/52.38 0 ==> 0
% 51.95/52.38 1 ==> 1
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 resolution: (10995) {G1,W11,D3,L3,V3,M3} { ! convergent_lines( X, Y ),
% 51.95/52.38 distinct_points( Z, intersection_point( X, Y ) ), ! apart_point_and_line
% 51.95/52.38 ( Z, Y ) }.
% 51.95/52.38 parent0[1]: (9) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 51.95/52.38 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 51.95/52.38 parent1[1]: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ),
% 51.95/52.38 apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 X := X
% 51.95/52.38 Y := Y
% 51.95/52.38 end
% 51.95/52.38 substitution1:
% 51.95/52.38 X := Z
% 51.95/52.38 Y := Y
% 51.95/52.38 Z := intersection_point( X, Y )
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 subsumption: (81) {G1,W11,D3,L3,V3,M1} R(11,9) { distinct_points( X,
% 51.95/52.38 intersection_point( Y, Z ) ), ! convergent_lines( Y, Z ), !
% 51.95/52.38 apart_point_and_line( X, Z ) }.
% 51.95/52.38 parent0: (10995) {G1,W11,D3,L3,V3,M3} { ! convergent_lines( X, Y ),
% 51.95/52.38 distinct_points( Z, intersection_point( X, Y ) ), ! apart_point_and_line
% 51.95/52.38 ( Z, Y ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 X := Y
% 51.95/52.38 Y := Z
% 51.95/52.38 Z := X
% 51.95/52.38 end
% 51.95/52.38 permutation0:
% 51.95/52.38 0 ==> 1
% 51.95/52.38 1 ==> 0
% 51.95/52.38 2 ==> 2
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 resolution: (10997) {G2,W6,D2,L2,V1,M2} { convergent_lines( X, skol3 ),
% 51.95/52.38 convergent_lines( X, skol4 ) }.
% 51.95/52.38 parent0[0]: (33) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 51.95/52.38 convergent_lines( X, Y ) }.
% 51.95/52.38 parent1[1]: (71) {G2,W6,D2,L2,V1,M2} R(32,33) { convergent_lines( X, skol4
% 51.95/52.38 ), convergent_lines( skol3, X ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 X := X
% 51.95/52.38 Y := skol3
% 51.95/52.38 end
% 51.95/52.38 substitution1:
% 51.95/52.38 X := X
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 subsumption: (84) {G3,W6,D2,L2,V1,M1} R(71,33) { convergent_lines( X, skol3
% 51.95/52.38 ), convergent_lines( X, skol4 ) }.
% 51.95/52.38 parent0: (10997) {G2,W6,D2,L2,V1,M2} { convergent_lines( X, skol3 ),
% 51.95/52.38 convergent_lines( X, skol4 ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 X := X
% 51.95/52.38 end
% 51.95/52.38 permutation0:
% 51.95/52.38 0 ==> 0
% 51.95/52.38 1 ==> 1
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 resolution: (10998) {G1,W9,D2,L3,V3,M3} { distinct_lines( Y, X ), !
% 51.95/52.38 convergent_lines( Z, X ), convergent_lines( Z, Y ) }.
% 51.95/52.38 parent0[0]: (26) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 51.95/52.38 distinct_lines( X, Y ) }.
% 51.95/52.38 parent1[2]: (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ),
% 51.95/52.38 convergent_lines( X, Z ), distinct_lines( Y, Z ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 X := Y
% 51.95/52.38 Y := X
% 51.95/52.38 end
% 51.95/52.38 substitution1:
% 51.95/52.38 X := Z
% 51.95/52.38 Y := X
% 51.95/52.38 Z := Y
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 subsumption: (120) {G2,W9,D2,L3,V3,M1} R(13,26) { ! convergent_lines( X, Y
% 51.95/52.38 ), convergent_lines( X, Z ), distinct_lines( Z, Y ) }.
% 51.95/52.38 parent0: (10998) {G1,W9,D2,L3,V3,M3} { distinct_lines( Y, X ), !
% 51.95/52.38 convergent_lines( Z, X ), convergent_lines( Z, Y ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 X := Y
% 51.95/52.38 Y := Z
% 51.95/52.38 Z := X
% 51.95/52.38 end
% 51.95/52.38 permutation0:
% 51.95/52.38 0 ==> 2
% 51.95/52.38 1 ==> 0
% 51.95/52.38 2 ==> 1
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 resolution: (10999) {G1,W20,D3,L6,V3,M6} { ! convergent_lines( X, Y ), !
% 51.95/52.38 distinct_points( intersection_point( X, Y ), Z ), ! distinct_lines( Y, X
% 51.95/52.38 ), ! convergent_lines( X, Y ), apart_point_and_line( Z, Y ),
% 51.95/52.38 apart_point_and_line( Z, X ) }.
% 51.95/52.38 parent0[1]: (9) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 51.95/52.38 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 51.95/52.38 parent1[3]: (48) {G1,W22,D3,L6,V4,M3} R(10,8) { ! distinct_points(
% 51.95/52.38 intersection_point( X, Y ), Z ), ! distinct_lines( T, X ), !
% 51.95/52.38 convergent_lines( X, Y ), apart_point_and_line( intersection_point( X, Y
% 51.95/52.38 ), T ), apart_point_and_line( Z, T ), apart_point_and_line( Z, X ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 X := X
% 51.95/52.38 Y := Y
% 51.95/52.38 end
% 51.95/52.38 substitution1:
% 51.95/52.38 X := X
% 51.95/52.38 Y := Y
% 51.95/52.38 Z := Z
% 51.95/52.38 T := Y
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 factor: (11006) {G1,W17,D3,L5,V3,M5} { ! convergent_lines( X, Y ), !
% 51.95/52.38 distinct_points( intersection_point( X, Y ), Z ), ! distinct_lines( Y, X
% 51.95/52.38 ), apart_point_and_line( Z, Y ), apart_point_and_line( Z, X ) }.
% 51.95/52.38 parent0[0, 3]: (10999) {G1,W20,D3,L6,V3,M6} { ! convergent_lines( X, Y ),
% 51.95/52.38 ! distinct_points( intersection_point( X, Y ), Z ), ! distinct_lines( Y,
% 51.95/52.38 X ), ! convergent_lines( X, Y ), apart_point_and_line( Z, Y ),
% 51.95/52.38 apart_point_and_line( Z, X ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 X := X
% 51.95/52.38 Y := Y
% 51.95/52.38 Z := Z
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 subsumption: (572) {G2,W17,D3,L5,V3,M2} R(48,9);f { ! distinct_points(
% 51.95/52.38 intersection_point( X, Y ), Z ), ! convergent_lines( X, Y ), !
% 51.95/52.38 distinct_lines( Y, X ), apart_point_and_line( Z, X ),
% 51.95/52.38 apart_point_and_line( Z, Y ) }.
% 51.95/52.38 parent0: (11006) {G1,W17,D3,L5,V3,M5} { ! convergent_lines( X, Y ), !
% 51.95/52.38 distinct_points( intersection_point( X, Y ), Z ), ! distinct_lines( Y, X
% 51.95/52.38 ), apart_point_and_line( Z, Y ), apart_point_and_line( Z, X ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 X := X
% 51.95/52.38 Y := Y
% 51.95/52.38 Z := Z
% 51.95/52.38 end
% 51.95/52.38 permutation0:
% 51.95/52.38 0 ==> 1
% 51.95/52.38 1 ==> 0
% 51.95/52.38 2 ==> 2
% 51.95/52.38 3 ==> 4
% 51.95/52.38 4 ==> 3
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 resolution: (11009) {G1,W15,D3,L3,V1,M3} { distinct_points(
% 51.95/52.38 intersection_point( skol3, skol4 ), intersection_point( X, skol2 ) ), !
% 51.95/52.38 convergent_lines( X, skol2 ), apart_point_and_line( intersection_point(
% 51.95/52.38 skol3, skol4 ), skol1 ) }.
% 51.95/52.38 parent0[2]: (81) {G1,W11,D3,L3,V3,M1} R(11,9) { distinct_points( X,
% 51.95/52.38 intersection_point( Y, Z ) ), ! convergent_lines( Y, Z ), !
% 51.95/52.38 apart_point_and_line( X, Z ) }.
% 51.95/52.38 parent1[1]: (18) {G0,W10,D3,L2,V0,M1} I { apart_point_and_line(
% 51.95/52.38 intersection_point( skol3, skol4 ), skol1 ), apart_point_and_line(
% 51.95/52.38 intersection_point( skol3, skol4 ), skol2 ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 X := intersection_point( skol3, skol4 )
% 51.95/52.38 Y := X
% 51.95/52.38 Z := skol2
% 51.95/52.38 end
% 51.95/52.38 substitution1:
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 subsumption: (1307) {G2,W15,D3,L3,V1,M1} R(81,18) { ! convergent_lines( X,
% 51.95/52.38 skol2 ), distinct_points( intersection_point( skol3, skol4 ),
% 51.95/52.38 intersection_point( X, skol2 ) ), apart_point_and_line(
% 51.95/52.38 intersection_point( skol3, skol4 ), skol1 ) }.
% 51.95/52.38 parent0: (11009) {G1,W15,D3,L3,V1,M3} { distinct_points(
% 51.95/52.38 intersection_point( skol3, skol4 ), intersection_point( X, skol2 ) ), !
% 51.95/52.38 convergent_lines( X, skol2 ), apart_point_and_line( intersection_point(
% 51.95/52.38 skol3, skol4 ), skol1 ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 X := X
% 51.95/52.38 end
% 51.95/52.38 permutation0:
% 51.95/52.38 0 ==> 1
% 51.95/52.38 1 ==> 0
% 51.95/52.38 2 ==> 2
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 resolution: (11010) {G1,W18,D3,L4,V1,M4} { ! distinct_points(
% 51.95/52.38 intersection_point( skol3, X ), intersection_point( skol1, skol2 ) ), !
% 51.95/52.38 convergent_lines( skol3, X ), ! distinct_lines( X, skol3 ),
% 51.95/52.38 apart_point_and_line( intersection_point( skol1, skol2 ), X ) }.
% 51.95/52.38 parent0[0]: (16) {G0,W5,D3,L1,V0,M1} I { ! apart_point_and_line(
% 51.95/52.38 intersection_point( skol1, skol2 ), skol3 ) }.
% 51.95/52.38 parent1[3]: (572) {G2,W17,D3,L5,V3,M2} R(48,9);f { ! distinct_points(
% 51.95/52.38 intersection_point( X, Y ), Z ), ! convergent_lines( X, Y ), !
% 51.95/52.38 distinct_lines( Y, X ), apart_point_and_line( Z, X ),
% 51.95/52.38 apart_point_and_line( Z, Y ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 end
% 51.95/52.38 substitution1:
% 51.95/52.38 X := skol3
% 51.95/52.38 Y := X
% 51.95/52.38 Z := intersection_point( skol1, skol2 )
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 subsumption: (8945) {G3,W18,D3,L4,V1,M1} R(572,16) { ! convergent_lines(
% 51.95/52.38 skol3, X ), ! distinct_points( intersection_point( skol3, X ),
% 51.95/52.38 intersection_point( skol1, skol2 ) ), ! distinct_lines( X, skol3 ),
% 51.95/52.38 apart_point_and_line( intersection_point( skol1, skol2 ), X ) }.
% 51.95/52.38 parent0: (11010) {G1,W18,D3,L4,V1,M4} { ! distinct_points(
% 51.95/52.38 intersection_point( skol3, X ), intersection_point( skol1, skol2 ) ), !
% 51.95/52.38 convergent_lines( skol3, X ), ! distinct_lines( X, skol3 ),
% 51.95/52.38 apart_point_and_line( intersection_point( skol1, skol2 ), X ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 X := X
% 51.95/52.38 end
% 51.95/52.38 permutation0:
% 51.95/52.38 0 ==> 1
% 51.95/52.38 1 ==> 0
% 51.95/52.38 2 ==> 2
% 51.95/52.38 3 ==> 3
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 resolution: (11012) {G1,W18,D3,L4,V2,M4} { distinct_points(
% 51.95/52.38 intersection_point( skol3, skol4 ), X ), apart_point_and_line( X, skol1 )
% 51.95/52.38 , ! convergent_lines( Y, skol2 ), distinct_points( intersection_point(
% 51.95/52.38 skol3, skol4 ), intersection_point( Y, skol2 ) ) }.
% 51.95/52.38 parent0[2]: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ),
% 51.95/52.38 apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 51.95/52.38 parent1[2]: (1307) {G2,W15,D3,L3,V1,M1} R(81,18) { ! convergent_lines( X,
% 51.95/52.38 skol2 ), distinct_points( intersection_point( skol3, skol4 ),
% 51.95/52.38 intersection_point( X, skol2 ) ), apart_point_and_line(
% 51.95/52.38 intersection_point( skol3, skol4 ), skol1 ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 X := intersection_point( skol3, skol4 )
% 51.95/52.38 Y := skol1
% 51.95/52.38 Z := X
% 51.95/52.38 end
% 51.95/52.38 substitution1:
% 51.95/52.38 X := Y
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 subsumption: (9733) {G3,W18,D3,L4,V2,M1} R(1307,11) { ! convergent_lines( X
% 51.95/52.38 , skol2 ), distinct_points( intersection_point( skol3, skol4 ),
% 51.95/52.38 intersection_point( X, skol2 ) ), distinct_points( intersection_point(
% 51.95/52.38 skol3, skol4 ), Y ), apart_point_and_line( Y, skol1 ) }.
% 51.95/52.38 parent0: (11012) {G1,W18,D3,L4,V2,M4} { distinct_points(
% 51.95/52.38 intersection_point( skol3, skol4 ), X ), apart_point_and_line( X, skol1 )
% 51.95/52.38 , ! convergent_lines( Y, skol2 ), distinct_points( intersection_point(
% 51.95/52.38 skol3, skol4 ), intersection_point( Y, skol2 ) ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 X := Y
% 51.95/52.38 Y := X
% 51.95/52.38 end
% 51.95/52.38 permutation0:
% 51.95/52.38 0 ==> 2
% 51.95/52.38 1 ==> 3
% 51.95/52.38 2 ==> 0
% 51.95/52.38 3 ==> 1
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 factor: (11014) {G3,W15,D3,L3,V1,M3} { ! convergent_lines( X, skol2 ),
% 51.95/52.38 distinct_points( intersection_point( skol3, skol4 ), intersection_point(
% 51.95/52.38 X, skol2 ) ), apart_point_and_line( intersection_point( X, skol2 ), skol1
% 51.95/52.38 ) }.
% 51.95/52.38 parent0[1, 2]: (9733) {G3,W18,D3,L4,V2,M1} R(1307,11) { ! convergent_lines
% 51.95/52.38 ( X, skol2 ), distinct_points( intersection_point( skol3, skol4 ),
% 51.95/52.38 intersection_point( X, skol2 ) ), distinct_points( intersection_point(
% 51.95/52.38 skol3, skol4 ), Y ), apart_point_and_line( Y, skol1 ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 X := X
% 51.95/52.38 Y := intersection_point( X, skol2 )
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 subsumption: (9734) {G4,W15,D3,L3,V1,M1} F(9733) { ! convergent_lines( X,
% 51.95/52.38 skol2 ), distinct_points( intersection_point( skol3, skol4 ),
% 51.95/52.38 intersection_point( X, skol2 ) ), apart_point_and_line(
% 51.95/52.38 intersection_point( X, skol2 ), skol1 ) }.
% 51.95/52.38 parent0: (11014) {G3,W15,D3,L3,V1,M3} { ! convergent_lines( X, skol2 ),
% 51.95/52.38 distinct_points( intersection_point( skol3, skol4 ), intersection_point(
% 51.95/52.38 X, skol2 ) ), apart_point_and_line( intersection_point( X, skol2 ), skol1
% 51.95/52.38 ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 X := X
% 51.95/52.38 end
% 51.95/52.38 permutation0:
% 51.95/52.38 0 ==> 0
% 51.95/52.38 1 ==> 1
% 51.95/52.38 2 ==> 2
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 resolution: (11015) {G1,W13,D3,L3,V0,M3} { ! convergent_lines( skol1,
% 51.95/52.38 skol2 ), ! convergent_lines( skol1, skol2 ), distinct_points(
% 51.95/52.38 intersection_point( skol3, skol4 ), intersection_point( skol1, skol2 ) )
% 51.95/52.38 }.
% 51.95/52.38 parent0[1]: (8) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 51.95/52.38 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 51.95/52.38 parent1[2]: (9734) {G4,W15,D3,L3,V1,M1} F(9733) { ! convergent_lines( X,
% 51.95/52.38 skol2 ), distinct_points( intersection_point( skol3, skol4 ),
% 51.95/52.38 intersection_point( X, skol2 ) ), apart_point_and_line(
% 51.95/52.38 intersection_point( X, skol2 ), skol1 ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 X := skol1
% 51.95/52.38 Y := skol2
% 51.95/52.38 end
% 51.95/52.38 substitution1:
% 51.95/52.38 X := skol1
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 factor: (11016) {G1,W10,D3,L2,V0,M2} { ! convergent_lines( skol1, skol2 )
% 51.95/52.38 , distinct_points( intersection_point( skol3, skol4 ), intersection_point
% 51.95/52.38 ( skol1, skol2 ) ) }.
% 51.95/52.38 parent0[0, 1]: (11015) {G1,W13,D3,L3,V0,M3} { ! convergent_lines( skol1,
% 51.95/52.38 skol2 ), ! convergent_lines( skol1, skol2 ), distinct_points(
% 51.95/52.38 intersection_point( skol3, skol4 ), intersection_point( skol1, skol2 ) )
% 51.95/52.38 }.
% 51.95/52.38 substitution0:
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 resolution: (11018) {G1,W7,D3,L1,V0,M1} { distinct_points(
% 51.95/52.38 intersection_point( skol3, skol4 ), intersection_point( skol1, skol2 ) )
% 51.95/52.38 }.
% 51.95/52.38 parent0[0]: (11016) {G1,W10,D3,L2,V0,M2} { ! convergent_lines( skol1,
% 51.95/52.38 skol2 ), distinct_points( intersection_point( skol3, skol4 ),
% 51.95/52.38 intersection_point( skol1, skol2 ) ) }.
% 51.95/52.38 parent1[0]: (14) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 )
% 51.95/52.38 }.
% 51.95/52.38 substitution0:
% 51.95/52.38 end
% 51.95/52.38 substitution1:
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 subsumption: (9787) {G5,W7,D3,L1,V0,M1} R(9734,8);f;r(14) { distinct_points
% 51.95/52.38 ( intersection_point( skol3, skol4 ), intersection_point( skol1, skol2 )
% 51.95/52.38 ) }.
% 51.95/52.38 parent0: (11018) {G1,W7,D3,L1,V0,M1} { distinct_points( intersection_point
% 51.95/52.38 ( skol3, skol4 ), intersection_point( skol1, skol2 ) ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 end
% 51.95/52.38 permutation0:
% 51.95/52.38 0 ==> 0
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 resolution: (11019) {G1,W13,D3,L3,V0,M3} { ! convergent_lines( skol3,
% 51.95/52.38 skol4 ), ! distinct_points( intersection_point( skol3, skol4 ),
% 51.95/52.38 intersection_point( skol1, skol2 ) ), ! distinct_lines( skol4, skol3 )
% 51.95/52.38 }.
% 51.95/52.38 parent0[0]: (17) {G0,W5,D3,L1,V0,M1} I { ! apart_point_and_line(
% 51.95/52.38 intersection_point( skol1, skol2 ), skol4 ) }.
% 51.95/52.38 parent1[3]: (8945) {G3,W18,D3,L4,V1,M1} R(572,16) { ! convergent_lines(
% 51.95/52.38 skol3, X ), ! distinct_points( intersection_point( skol3, X ),
% 51.95/52.38 intersection_point( skol1, skol2 ) ), ! distinct_lines( X, skol3 ),
% 51.95/52.38 apart_point_and_line( intersection_point( skol1, skol2 ), X ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 end
% 51.95/52.38 substitution1:
% 51.95/52.38 X := skol4
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 resolution: (11020) {G1,W10,D3,L2,V0,M2} { ! distinct_points(
% 51.95/52.38 intersection_point( skol3, skol4 ), intersection_point( skol1, skol2 ) )
% 51.95/52.38 , ! distinct_lines( skol4, skol3 ) }.
% 51.95/52.38 parent0[0]: (11019) {G1,W13,D3,L3,V0,M3} { ! convergent_lines( skol3,
% 51.95/52.38 skol4 ), ! distinct_points( intersection_point( skol3, skol4 ),
% 51.95/52.38 intersection_point( skol1, skol2 ) ), ! distinct_lines( skol4, skol3 )
% 51.95/52.38 }.
% 51.95/52.38 parent1[0]: (15) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol3, skol4 )
% 51.95/52.38 }.
% 51.95/52.38 substitution0:
% 51.95/52.38 end
% 51.95/52.38 substitution1:
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 subsumption: (10466) {G4,W10,D3,L2,V0,M1} R(8945,17);r(15) { !
% 51.95/52.38 distinct_points( intersection_point( skol3, skol4 ), intersection_point(
% 51.95/52.38 skol1, skol2 ) ), ! distinct_lines( skol4, skol3 ) }.
% 51.95/52.38 parent0: (11020) {G1,W10,D3,L2,V0,M2} { ! distinct_points(
% 51.95/52.38 intersection_point( skol3, skol4 ), intersection_point( skol1, skol2 ) )
% 51.95/52.38 , ! distinct_lines( skol4, skol3 ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 end
% 51.95/52.38 permutation0:
% 51.95/52.38 0 ==> 0
% 51.95/52.38 1 ==> 1
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 resolution: (11021) {G5,W3,D2,L1,V0,M1} { ! distinct_lines( skol4, skol3 )
% 51.95/52.38 }.
% 51.95/52.38 parent0[0]: (10466) {G4,W10,D3,L2,V0,M1} R(8945,17);r(15) { !
% 51.95/52.38 distinct_points( intersection_point( skol3, skol4 ), intersection_point(
% 51.95/52.38 skol1, skol2 ) ), ! distinct_lines( skol4, skol3 ) }.
% 51.95/52.38 parent1[0]: (9787) {G5,W7,D3,L1,V0,M1} R(9734,8);f;r(14) { distinct_points
% 51.95/52.38 ( intersection_point( skol3, skol4 ), intersection_point( skol1, skol2 )
% 51.95/52.38 ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 end
% 51.95/52.38 substitution1:
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 subsumption: (10467) {G6,W3,D2,L1,V0,M1} S(10466);r(9787) { !
% 51.95/52.38 distinct_lines( skol4, skol3 ) }.
% 51.95/52.38 parent0: (11021) {G5,W3,D2,L1,V0,M1} { ! distinct_lines( skol4, skol3 )
% 51.95/52.38 }.
% 51.95/52.38 substitution0:
% 51.95/52.38 end
% 51.95/52.38 permutation0:
% 51.95/52.38 0 ==> 0
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 resolution: (11022) {G3,W6,D2,L2,V1,M2} { ! convergent_lines( X, skol3 ),
% 51.95/52.38 convergent_lines( X, skol4 ) }.
% 51.95/52.38 parent0[0]: (10467) {G6,W3,D2,L1,V0,M1} S(10466);r(9787) { ! distinct_lines
% 51.95/52.38 ( skol4, skol3 ) }.
% 51.95/52.38 parent1[2]: (120) {G2,W9,D2,L3,V3,M1} R(13,26) { ! convergent_lines( X, Y )
% 51.95/52.38 , convergent_lines( X, Z ), distinct_lines( Z, Y ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 end
% 51.95/52.38 substitution1:
% 51.95/52.38 X := X
% 51.95/52.38 Y := skol3
% 51.95/52.38 Z := skol4
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 resolution: (11023) {G4,W6,D2,L2,V1,M2} { convergent_lines( X, skol4 ),
% 51.95/52.38 convergent_lines( X, skol4 ) }.
% 51.95/52.38 parent0[0]: (11022) {G3,W6,D2,L2,V1,M2} { ! convergent_lines( X, skol3 ),
% 51.95/52.38 convergent_lines( X, skol4 ) }.
% 51.95/52.38 parent1[0]: (84) {G3,W6,D2,L2,V1,M1} R(71,33) { convergent_lines( X, skol3
% 51.95/52.38 ), convergent_lines( X, skol4 ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 X := X
% 51.95/52.38 end
% 51.95/52.38 substitution1:
% 51.95/52.38 X := X
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 factor: (11024) {G4,W3,D2,L1,V1,M1} { convergent_lines( X, skol4 ) }.
% 51.95/52.38 parent0[0, 1]: (11023) {G4,W6,D2,L2,V1,M2} { convergent_lines( X, skol4 )
% 51.95/52.38 , convergent_lines( X, skol4 ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 X := X
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 subsumption: (10834) {G7,W3,D2,L1,V1,M1} R(10467,120);r(84) {
% 51.95/52.38 convergent_lines( X, skol4 ) }.
% 51.95/52.38 parent0: (11024) {G4,W3,D2,L1,V1,M1} { convergent_lines( X, skol4 ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 X := X
% 51.95/52.38 end
% 51.95/52.38 permutation0:
% 51.95/52.38 0 ==> 0
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 resolution: (11025) {G1,W0,D0,L0,V0,M0} { }.
% 51.95/52.38 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 51.95/52.38 parent1[0]: (10834) {G7,W3,D2,L1,V1,M1} R(10467,120);r(84) {
% 51.95/52.38 convergent_lines( X, skol4 ) }.
% 51.95/52.38 substitution0:
% 51.95/52.38 X := skol4
% 51.95/52.38 end
% 51.95/52.38 substitution1:
% 51.95/52.38 X := skol4
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 subsumption: (10875) {G8,W0,D0,L0,V0,M0} R(10834,2) { }.
% 51.95/52.38 parent0: (11025) {G1,W0,D0,L0,V0,M0} { }.
% 51.95/52.38 substitution0:
% 51.95/52.38 end
% 51.95/52.38 permutation0:
% 51.95/52.38 end
% 51.95/52.38
% 51.95/52.38 Proof check complete!
% 51.95/52.38
% 51.95/52.38 Memory use:
% 51.95/52.38
% 51.95/52.38 space for terms: 181052
% 51.95/52.38 space for clauses: 370097
% 51.95/52.38
% 51.95/52.38
% 51.95/52.38 clauses generated: 4263873
% 51.95/52.38 clauses kept: 10876
% 51.95/52.38 clauses selected: 10039
% 51.95/52.38 clauses deleted: 232
% 51.95/52.38 clauses inuse deleted: 132
% 51.95/52.38
% 51.95/52.38 subsentry: 27228982
% 51.95/52.38 literals s-matched: 15909568
% 51.95/52.38 literals matched: 15909490
% 51.95/52.38 full subsumption: 14758594
% 51.95/52.38
% 51.95/52.38 checksum: -1073812921
% 51.95/52.38
% 51.95/52.38
% 51.95/52.38 Bliksem ended
%------------------------------------------------------------------------------