TSTP Solution File: GEO175+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO175+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n006.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 02:52:15 EDT 2022
% Result : Theorem 2.30s 2.68s
% Output : Refutation 2.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO175+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : bliksem %s
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Sat Jun 18 01:23:10 EDT 2022
% 0.13/0.33 % CPUTime :
% 2.30/2.68 *** allocated 10000 integers for termspace/termends
% 2.30/2.68 *** allocated 10000 integers for clauses
% 2.30/2.68 *** allocated 10000 integers for justifications
% 2.30/2.68 Bliksem 1.12
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 Automatic Strategy Selection
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 Clauses:
% 2.30/2.68
% 2.30/2.68 { ! distinct_points( X, X ) }.
% 2.30/2.68 { ! distinct_lines( X, X ) }.
% 2.30/2.68 { ! convergent_lines( X, X ) }.
% 2.30/2.68 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 2.30/2.68 ) }.
% 2.30/2.68 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 2.30/2.68 }.
% 2.30/2.68 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 2.30/2.68 , Z ) }.
% 2.30/2.68 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 2.30/2.68 , Y ) ) }.
% 2.30/2.68 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 2.30/2.68 , Y ) ) }.
% 2.30/2.68 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 2.30/2.68 , Y ), X ) }.
% 2.30/2.68 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 2.30/2.68 , Y ), Y ) }.
% 2.30/2.68 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 2.30/2.68 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 2.30/2.68 apart_point_and_line( Y, T ) }.
% 2.30/2.68 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 2.30/2.68 apart_point_and_line( Z, Y ) }.
% 2.30/2.68 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 2.30/2.68 apart_point_and_line( X, Z ) }.
% 2.30/2.68 { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X,
% 2.30/2.68 Z ) }.
% 2.30/2.68 { distinct_points( skol1, skol4 ) }.
% 2.30/2.68 { convergent_lines( skol2, skol3 ) }.
% 2.30/2.68 { distinct_points( skol1, intersection_point( skol2, skol3 ) ) }.
% 2.30/2.68 { ! apart_point_and_line( skol1, skol2 ) }.
% 2.30/2.68 { ! apart_point_and_line( skol1, skol3 ) }.
% 2.30/2.68
% 2.30/2.68 percentage equality = 0.000000, percentage horn = 0.631579
% 2.30/2.68 This a non-horn, non-equality problem
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 Options Used:
% 2.30/2.68
% 2.30/2.68 useres = 1
% 2.30/2.68 useparamod = 0
% 2.30/2.68 useeqrefl = 0
% 2.30/2.68 useeqfact = 0
% 2.30/2.68 usefactor = 1
% 2.30/2.68 usesimpsplitting = 0
% 2.30/2.68 usesimpdemod = 0
% 2.30/2.68 usesimpres = 3
% 2.30/2.68
% 2.30/2.68 resimpinuse = 1000
% 2.30/2.68 resimpclauses = 20000
% 2.30/2.68 substype = standard
% 2.30/2.68 backwardsubs = 1
% 2.30/2.68 selectoldest = 5
% 2.30/2.68
% 2.30/2.68 litorderings [0] = split
% 2.30/2.68 litorderings [1] = liftord
% 2.30/2.68
% 2.30/2.68 termordering = none
% 2.30/2.68
% 2.30/2.68 litapriori = 1
% 2.30/2.68 termapriori = 0
% 2.30/2.68 litaposteriori = 0
% 2.30/2.68 termaposteriori = 0
% 2.30/2.68 demodaposteriori = 0
% 2.30/2.68 ordereqreflfact = 0
% 2.30/2.68
% 2.30/2.68 litselect = none
% 2.30/2.68
% 2.30/2.68 maxweight = 15
% 2.30/2.68 maxdepth = 30000
% 2.30/2.68 maxlength = 115
% 2.30/2.68 maxnrvars = 195
% 2.30/2.68 excuselevel = 1
% 2.30/2.68 increasemaxweight = 1
% 2.30/2.68
% 2.30/2.68 maxselected = 10000000
% 2.30/2.68 maxnrclauses = 10000000
% 2.30/2.68
% 2.30/2.68 showgenerated = 0
% 2.30/2.68 showkept = 0
% 2.30/2.68 showselected = 0
% 2.30/2.68 showdeleted = 0
% 2.30/2.68 showresimp = 1
% 2.30/2.68 showstatus = 2000
% 2.30/2.68
% 2.30/2.68 prologoutput = 0
% 2.30/2.68 nrgoals = 5000000
% 2.30/2.68 totalproof = 1
% 2.30/2.68
% 2.30/2.68 Symbols occurring in the translation:
% 2.30/2.68
% 2.30/2.68 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 2.30/2.68 . [1, 2] (w:1, o:20, a:1, s:1, b:0),
% 2.30/2.68 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 2.30/2.68 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.30/2.68 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.30/2.68 distinct_points [36, 2] (w:1, o:45, a:1, s:1, b:0),
% 2.30/2.68 distinct_lines [37, 2] (w:1, o:46, a:1, s:1, b:0),
% 2.30/2.68 convergent_lines [38, 2] (w:1, o:44, a:1, s:1, b:0),
% 2.30/2.68 line_connecting [41, 2] (w:1, o:47, a:1, s:1, b:0),
% 2.30/2.68 apart_point_and_line [42, 2] (w:1, o:48, a:1, s:1, b:0),
% 2.30/2.68 intersection_point [43, 2] (w:1, o:49, a:1, s:1, b:0),
% 2.30/2.68 skol1 [46, 0] (w:1, o:11, a:1, s:1, b:0),
% 2.30/2.68 skol2 [47, 0] (w:1, o:12, a:1, s:1, b:0),
% 2.30/2.68 skol3 [48, 0] (w:1, o:13, a:1, s:1, b:0),
% 2.30/2.68 skol4 [49, 0] (w:1, o:14, a:1, s:1, b:0).
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 Starting Search:
% 2.30/2.68
% 2.30/2.68 *** allocated 15000 integers for clauses
% 2.30/2.68 *** allocated 22500 integers for clauses
% 2.30/2.68 *** allocated 33750 integers for clauses
% 2.30/2.68 *** allocated 15000 integers for termspace/termends
% 2.30/2.68 Resimplifying inuse:
% 2.30/2.68 Done
% 2.30/2.68
% 2.30/2.68 Failed to find proof!
% 2.30/2.68 maxweight = 15
% 2.30/2.68 maxnrclauses = 10000000
% 2.30/2.68 Generated: 136122
% 2.30/2.68 Kept: 799
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 The strategy used was not complete!
% 2.30/2.68
% 2.30/2.68 Increased maxweight to 16
% 2.30/2.68
% 2.30/2.68 Starting Search:
% 2.30/2.68
% 2.30/2.68 *** allocated 50625 integers for clauses
% 2.30/2.68 *** allocated 22500 integers for termspace/termends
% 2.30/2.68 Resimplifying inuse:
% 2.30/2.68 Done
% 2.30/2.68
% 2.30/2.68 *** allocated 75937 integers for clauses
% 2.30/2.68 *** allocated 33750 integers for termspace/termends
% 2.30/2.68
% 2.30/2.68 Bliksems!, er is een bewijs:
% 2.30/2.68 % SZS status Theorem
% 2.30/2.68 % SZS output start Refutation
% 2.30/2.68
% 2.30/2.68 (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 2.30/2.68 (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 2.30/2.68 (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 2.30/2.68 (3) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ), distinct_points( Y, Z
% 2.30/2.68 ), ! distinct_points( X, Y ) }.
% 2.30/2.68 (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 2.30/2.68 , ! distinct_lines( X, Y ) }.
% 2.30/2.68 (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), convergent_lines( Y,
% 2.30/2.68 Z ), ! convergent_lines( X, Y ) }.
% 2.30/2.68 (8) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 2.30/2.68 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 2.30/2.68 (9) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 2.30/2.68 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 2.30/2.68 (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! distinct_lines(
% 2.30/2.68 Z, T ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 2.30/2.68 apart_point_and_line( Y, T ), apart_point_and_line( X, Z ) }.
% 2.30/2.68 (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), apart_point_and_line
% 2.30/2.68 ( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 2.30/2.68 (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ), convergent_lines(
% 2.30/2.68 X, Z ), distinct_lines( Y, Z ) }.
% 2.30/2.68 (15) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol2, skol3 ) }.
% 2.30/2.68 (16) {G0,W5,D3,L1,V0,M1} I { distinct_points( skol1, intersection_point(
% 2.30/2.68 skol2, skol3 ) ) }.
% 2.30/2.68 (17) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol1, skol2 ) }.
% 2.30/2.68 (18) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol1, skol3 ) }.
% 2.30/2.68 (21) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ),
% 2.30/2.68 distinct_points( X, Y ) }.
% 2.30/2.68 (30) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 2.30/2.68 ( X, Y ) }.
% 2.30/2.68 (37) {G1,W6,D2,L2,V1,M1} R(5,15) { convergent_lines( skol2, X ),
% 2.30/2.68 convergent_lines( skol3, X ) }.
% 2.30/2.68 (38) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 2.30/2.68 convergent_lines( X, Y ) }.
% 2.30/2.68 (42) {G2,W6,D2,L2,V1,M2} R(37,38) { convergent_lines( X, skol3 ),
% 2.30/2.68 convergent_lines( skol2, X ) }.
% 2.30/2.68 (44) {G3,W6,D2,L2,V1,M1} R(42,38) { convergent_lines( X, skol2 ),
% 2.30/2.68 convergent_lines( X, skol3 ) }.
% 2.30/2.68 (75) {G1,W15,D2,L5,V2,M3} R(10,17) { ! distinct_points( skol1, X ), !
% 2.30/2.68 distinct_lines( skol2, Y ), apart_point_and_line( X, skol2 ),
% 2.30/2.68 apart_point_and_line( X, Y ), apart_point_and_line( skol1, Y ) }.
% 2.30/2.68 (106) {G1,W6,D2,L2,V1,M1} R(11,18) { distinct_points( X, skol1 ), !
% 2.30/2.68 apart_point_and_line( X, skol3 ) }.
% 2.30/2.68 (108) {G2,W9,D2,L3,V2,M1} R(106,11) { distinct_points( X, skol1 ),
% 2.30/2.68 distinct_points( Y, X ), ! apart_point_and_line( Y, skol3 ) }.
% 2.30/2.68 (136) {G2,W9,D2,L3,V3,M1} R(13,30) { ! convergent_lines( X, Y ),
% 2.30/2.68 convergent_lines( X, Z ), distinct_lines( Z, Y ) }.
% 2.30/2.68 (235) {G3,W12,D2,L4,V3,M1} R(108,11) { distinct_points( X, skol1 ),
% 2.30/2.68 distinct_points( Y, X ), distinct_points( Z, Y ), ! apart_point_and_line
% 2.30/2.68 ( Z, skol3 ) }.
% 2.30/2.68 (236) {G4,W6,D2,L2,V1,M1} F(235);r(21) { distinct_points( skol1, X ), !
% 2.30/2.68 apart_point_and_line( X, skol3 ) }.
% 2.30/2.68 (686) {G5,W12,D2,L4,V1,M1} R(75,236);r(0) { ! distinct_points( skol1, X ),
% 2.30/2.68 ! distinct_lines( skol2, skol3 ), apart_point_and_line( X, skol2 ),
% 2.30/2.68 apart_point_and_line( X, skol3 ) }.
% 2.30/2.68 (852) {G6,W16,D3,L4,V1,M1} R(686,9) { ! distinct_points( skol1,
% 2.30/2.68 intersection_point( X, skol3 ) ), ! distinct_lines( skol2, skol3 ), !
% 2.30/2.68 convergent_lines( X, skol3 ), apart_point_and_line( intersection_point( X
% 2.30/2.68 , skol3 ), skol2 ) }.
% 2.30/2.68 (1322) {G7,W6,D2,L2,V0,M1} R(852,8);f;r(16) { ! convergent_lines( skol2,
% 2.30/2.68 skol3 ), ! distinct_lines( skol2, skol3 ) }.
% 2.30/2.68 (1323) {G8,W3,D2,L1,V0,M1} S(1322);r(15) { ! distinct_lines( skol2, skol3 )
% 2.30/2.68 }.
% 2.30/2.68 (1452) {G9,W3,D2,L1,V1,M1} R(1323,136);r(44) { convergent_lines( X, skol2 )
% 2.30/2.68 }.
% 2.30/2.68 (1469) {G10,W0,D0,L0,V0,M0} R(1452,2) { }.
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 % SZS output end Refutation
% 2.30/2.68 found a proof!
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 Unprocessed initial clauses:
% 2.30/2.68
% 2.30/2.68 (1471) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 2.30/2.68 (1472) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 2.30/2.68 (1473) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 2.30/2.68 (1474) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 2.30/2.68 , Z ), distinct_points( Y, Z ) }.
% 2.30/2.68 (1475) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X,
% 2.30/2.68 Z ), distinct_lines( Y, Z ) }.
% 2.30/2.68 (1476) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines
% 2.30/2.68 ( X, Z ), convergent_lines( Y, Z ) }.
% 2.30/2.68 (1477) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 2.30/2.68 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 2.30/2.68 (1478) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 2.30/2.68 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 2.30/2.68 (1479) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 2.30/2.68 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 2.30/2.68 (1480) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 2.30/2.68 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 2.30/2.68 (1481) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines
% 2.30/2.68 ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 2.30/2.68 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 2.30/2.68 (1482) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 2.30/2.68 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 2.30/2.68 (1483) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 2.30/2.68 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 2.30/2.68 (1484) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), distinct_lines( Y
% 2.30/2.68 , Z ), convergent_lines( X, Z ) }.
% 2.30/2.68 (1485) {G0,W3,D2,L1,V0,M1} { distinct_points( skol1, skol4 ) }.
% 2.30/2.68 (1486) {G0,W3,D2,L1,V0,M1} { convergent_lines( skol2, skol3 ) }.
% 2.30/2.68 (1487) {G0,W5,D3,L1,V0,M1} { distinct_points( skol1, intersection_point(
% 2.30/2.68 skol2, skol3 ) ) }.
% 2.30/2.68 (1488) {G0,W3,D2,L1,V0,M1} { ! apart_point_and_line( skol1, skol2 ) }.
% 2.30/2.68 (1489) {G0,W3,D2,L1,V0,M1} { ! apart_point_and_line( skol1, skol3 ) }.
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 Total Proof:
% 2.30/2.68
% 2.30/2.68 subsumption: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 2.30/2.68 parent0: (1471) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := X
% 2.30/2.68 end
% 2.30/2.68 permutation0:
% 2.30/2.68 0 ==> 0
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 2.30/2.68 parent0: (1472) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := X
% 2.30/2.68 end
% 2.30/2.68 permutation0:
% 2.30/2.68 0 ==> 0
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 subsumption: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 2.30/2.68 parent0: (1473) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := X
% 2.30/2.68 end
% 2.30/2.68 permutation0:
% 2.30/2.68 0 ==> 0
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 subsumption: (3) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ),
% 2.30/2.68 distinct_points( Y, Z ), ! distinct_points( X, Y ) }.
% 2.30/2.68 parent0: (1474) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ),
% 2.30/2.68 distinct_points( X, Z ), distinct_points( Y, Z ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := X
% 2.30/2.68 Y := Y
% 2.30/2.68 Z := Z
% 2.30/2.68 end
% 2.30/2.68 permutation0:
% 2.30/2.68 0 ==> 2
% 2.30/2.68 1 ==> 0
% 2.30/2.68 2 ==> 1
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 2.30/2.68 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 2.30/2.68 parent0: (1475) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ),
% 2.30/2.68 distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := X
% 2.30/2.68 Y := Y
% 2.30/2.68 Z := Z
% 2.30/2.68 end
% 2.30/2.68 permutation0:
% 2.30/2.68 0 ==> 2
% 2.30/2.68 1 ==> 0
% 2.30/2.68 2 ==> 1
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 subsumption: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 2.30/2.68 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 2.30/2.68 parent0: (1476) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 2.30/2.68 convergent_lines( X, Z ), convergent_lines( Y, Z ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := X
% 2.30/2.68 Y := Y
% 2.30/2.68 Z := Z
% 2.30/2.68 end
% 2.30/2.68 permutation0:
% 2.30/2.68 0 ==> 2
% 2.30/2.68 1 ==> 0
% 2.30/2.68 2 ==> 1
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 subsumption: (8) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 2.30/2.68 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 2.30/2.68 parent0: (1479) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 2.30/2.68 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := X
% 2.30/2.68 Y := Y
% 2.30/2.68 end
% 2.30/2.68 permutation0:
% 2.30/2.68 0 ==> 0
% 2.30/2.68 1 ==> 1
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 subsumption: (9) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 2.30/2.68 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 2.30/2.68 parent0: (1480) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 2.30/2.68 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := X
% 2.30/2.68 Y := Y
% 2.30/2.68 end
% 2.30/2.68 permutation0:
% 2.30/2.68 0 ==> 0
% 2.30/2.68 1 ==> 1
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 subsumption: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), !
% 2.30/2.68 distinct_lines( Z, T ), apart_point_and_line( X, T ),
% 2.30/2.68 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ),
% 2.30/2.68 apart_point_and_line( X, Z ) }.
% 2.30/2.68 parent0: (1481) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), !
% 2.30/2.68 distinct_lines( Z, T ), apart_point_and_line( X, Z ),
% 2.30/2.68 apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 2.30/2.68 apart_point_and_line( Y, T ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := X
% 2.30/2.68 Y := Y
% 2.30/2.68 Z := Z
% 2.30/2.68 T := T
% 2.30/2.68 end
% 2.30/2.68 permutation0:
% 2.30/2.68 0 ==> 0
% 2.30/2.68 1 ==> 1
% 2.30/2.68 2 ==> 5
% 2.30/2.68 3 ==> 2
% 2.30/2.68 4 ==> 3
% 2.30/2.68 5 ==> 4
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 subsumption: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ),
% 2.30/2.68 apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 2.30/2.68 parent0: (1482) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 2.30/2.68 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := X
% 2.30/2.68 Y := Y
% 2.30/2.68 Z := Z
% 2.30/2.68 end
% 2.30/2.68 permutation0:
% 2.30/2.68 0 ==> 2
% 2.30/2.68 1 ==> 0
% 2.30/2.68 2 ==> 1
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 subsumption: (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ),
% 2.30/2.68 convergent_lines( X, Z ), distinct_lines( Y, Z ) }.
% 2.30/2.68 parent0: (1484) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 2.30/2.68 distinct_lines( Y, Z ), convergent_lines( X, Z ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := X
% 2.30/2.68 Y := Y
% 2.30/2.68 Z := Z
% 2.30/2.68 end
% 2.30/2.68 permutation0:
% 2.30/2.68 0 ==> 0
% 2.30/2.68 1 ==> 2
% 2.30/2.68 2 ==> 1
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 subsumption: (15) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol2, skol3 )
% 2.30/2.68 }.
% 2.30/2.68 parent0: (1486) {G0,W3,D2,L1,V0,M1} { convergent_lines( skol2, skol3 ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 end
% 2.30/2.68 permutation0:
% 2.30/2.68 0 ==> 0
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 subsumption: (16) {G0,W5,D3,L1,V0,M1} I { distinct_points( skol1,
% 2.30/2.68 intersection_point( skol2, skol3 ) ) }.
% 2.30/2.68 parent0: (1487) {G0,W5,D3,L1,V0,M1} { distinct_points( skol1,
% 2.30/2.68 intersection_point( skol2, skol3 ) ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 end
% 2.30/2.68 permutation0:
% 2.30/2.68 0 ==> 0
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 subsumption: (17) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol1,
% 2.30/2.68 skol2 ) }.
% 2.30/2.68 parent0: (1488) {G0,W3,D2,L1,V0,M1} { ! apart_point_and_line( skol1, skol2
% 2.30/2.68 ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 end
% 2.30/2.68 permutation0:
% 2.30/2.68 0 ==> 0
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 subsumption: (18) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol1,
% 2.30/2.68 skol3 ) }.
% 2.30/2.68 parent0: (1489) {G0,W3,D2,L1,V0,M1} { ! apart_point_and_line( skol1, skol3
% 2.30/2.68 ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 end
% 2.30/2.68 permutation0:
% 2.30/2.68 0 ==> 0
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 resolution: (1565) {G1,W6,D2,L2,V2,M2} { distinct_points( Y, X ), !
% 2.30/2.68 distinct_points( X, Y ) }.
% 2.30/2.68 parent0[0]: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 2.30/2.68 parent1[0]: (3) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ),
% 2.30/2.68 distinct_points( Y, Z ), ! distinct_points( X, Y ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := X
% 2.30/2.68 end
% 2.30/2.68 substitution1:
% 2.30/2.68 X := X
% 2.30/2.68 Y := Y
% 2.30/2.68 Z := X
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 subsumption: (21) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ),
% 2.30/2.68 distinct_points( X, Y ) }.
% 2.30/2.68 parent0: (1565) {G1,W6,D2,L2,V2,M2} { distinct_points( Y, X ), !
% 2.30/2.68 distinct_points( X, Y ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := Y
% 2.30/2.68 Y := X
% 2.30/2.68 end
% 2.30/2.68 permutation0:
% 2.30/2.68 0 ==> 1
% 2.30/2.68 1 ==> 0
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 resolution: (1567) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 2.30/2.68 distinct_lines( X, Y ) }.
% 2.30/2.68 parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 2.30/2.68 parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 2.30/2.68 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := X
% 2.30/2.68 end
% 2.30/2.68 substitution1:
% 2.30/2.68 X := X
% 2.30/2.68 Y := Y
% 2.30/2.68 Z := X
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 subsumption: (30) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 2.30/2.68 distinct_lines( X, Y ) }.
% 2.30/2.68 parent0: (1567) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 2.30/2.68 distinct_lines( X, Y ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := Y
% 2.30/2.68 Y := X
% 2.30/2.68 end
% 2.30/2.68 permutation0:
% 2.30/2.68 0 ==> 1
% 2.30/2.68 1 ==> 0
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 resolution: (1569) {G1,W6,D2,L2,V1,M2} { convergent_lines( skol2, X ),
% 2.30/2.68 convergent_lines( skol3, X ) }.
% 2.30/2.68 parent0[2]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 2.30/2.68 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 2.30/2.68 parent1[0]: (15) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol2, skol3 )
% 2.30/2.68 }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := skol2
% 2.30/2.68 Y := skol3
% 2.30/2.68 Z := X
% 2.30/2.68 end
% 2.30/2.68 substitution1:
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 subsumption: (37) {G1,W6,D2,L2,V1,M1} R(5,15) { convergent_lines( skol2, X
% 2.30/2.68 ), convergent_lines( skol3, X ) }.
% 2.30/2.68 parent0: (1569) {G1,W6,D2,L2,V1,M2} { convergent_lines( skol2, X ),
% 2.30/2.68 convergent_lines( skol3, X ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := X
% 2.30/2.68 end
% 2.30/2.68 permutation0:
% 2.30/2.68 0 ==> 0
% 2.30/2.68 1 ==> 1
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 resolution: (1570) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 2.30/2.68 convergent_lines( X, Y ) }.
% 2.30/2.68 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 2.30/2.68 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 2.30/2.68 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := X
% 2.30/2.68 end
% 2.30/2.68 substitution1:
% 2.30/2.68 X := X
% 2.30/2.68 Y := Y
% 2.30/2.68 Z := X
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 subsumption: (38) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 2.30/2.68 convergent_lines( X, Y ) }.
% 2.30/2.68 parent0: (1570) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 2.30/2.68 convergent_lines( X, Y ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := Y
% 2.30/2.68 Y := X
% 2.30/2.68 end
% 2.30/2.68 permutation0:
% 2.30/2.68 0 ==> 1
% 2.30/2.68 1 ==> 0
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 resolution: (1573) {G2,W6,D2,L2,V1,M2} { convergent_lines( X, skol3 ),
% 2.30/2.68 convergent_lines( skol2, X ) }.
% 2.30/2.68 parent0[0]: (38) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 2.30/2.68 convergent_lines( X, Y ) }.
% 2.30/2.68 parent1[1]: (37) {G1,W6,D2,L2,V1,M1} R(5,15) { convergent_lines( skol2, X )
% 2.30/2.68 , convergent_lines( skol3, X ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := X
% 2.30/2.68 Y := skol3
% 2.30/2.68 end
% 2.30/2.68 substitution1:
% 2.30/2.68 X := X
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 subsumption: (42) {G2,W6,D2,L2,V1,M2} R(37,38) { convergent_lines( X, skol3
% 2.30/2.68 ), convergent_lines( skol2, X ) }.
% 2.30/2.68 parent0: (1573) {G2,W6,D2,L2,V1,M2} { convergent_lines( X, skol3 ),
% 2.30/2.68 convergent_lines( skol2, X ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := X
% 2.30/2.68 end
% 2.30/2.68 permutation0:
% 2.30/2.68 0 ==> 0
% 2.30/2.68 1 ==> 1
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 resolution: (1575) {G2,W6,D2,L2,V1,M2} { convergent_lines( X, skol2 ),
% 2.30/2.68 convergent_lines( X, skol3 ) }.
% 2.30/2.68 parent0[0]: (38) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 2.30/2.68 convergent_lines( X, Y ) }.
% 2.30/2.68 parent1[1]: (42) {G2,W6,D2,L2,V1,M2} R(37,38) { convergent_lines( X, skol3
% 2.30/2.68 ), convergent_lines( skol2, X ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := X
% 2.30/2.68 Y := skol2
% 2.30/2.68 end
% 2.30/2.68 substitution1:
% 2.30/2.68 X := X
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 subsumption: (44) {G3,W6,D2,L2,V1,M1} R(42,38) { convergent_lines( X, skol2
% 2.30/2.68 ), convergent_lines( X, skol3 ) }.
% 2.30/2.68 parent0: (1575) {G2,W6,D2,L2,V1,M2} { convergent_lines( X, skol2 ),
% 2.30/2.68 convergent_lines( X, skol3 ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := X
% 2.30/2.68 end
% 2.30/2.68 permutation0:
% 2.30/2.68 0 ==> 0
% 2.30/2.68 1 ==> 1
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 resolution: (1579) {G1,W15,D2,L5,V2,M5} { ! distinct_points( skol1, X ), !
% 2.30/2.68 distinct_lines( skol2, Y ), apart_point_and_line( skol1, Y ),
% 2.30/2.68 apart_point_and_line( X, skol2 ), apart_point_and_line( X, Y ) }.
% 2.30/2.68 parent0[0]: (17) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol1,
% 2.30/2.68 skol2 ) }.
% 2.30/2.68 parent1[5]: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), !
% 2.30/2.68 distinct_lines( Z, T ), apart_point_and_line( X, T ),
% 2.30/2.68 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ),
% 2.30/2.68 apart_point_and_line( X, Z ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 end
% 2.30/2.68 substitution1:
% 2.30/2.68 X := skol1
% 2.30/2.68 Y := X
% 2.30/2.68 Z := skol2
% 2.30/2.68 T := Y
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 subsumption: (75) {G1,W15,D2,L5,V2,M3} R(10,17) { ! distinct_points( skol1
% 2.30/2.68 , X ), ! distinct_lines( skol2, Y ), apart_point_and_line( X, skol2 ),
% 2.30/2.68 apart_point_and_line( X, Y ), apart_point_and_line( skol1, Y ) }.
% 2.30/2.68 parent0: (1579) {G1,W15,D2,L5,V2,M5} { ! distinct_points( skol1, X ), !
% 2.30/2.68 distinct_lines( skol2, Y ), apart_point_and_line( skol1, Y ),
% 2.30/2.68 apart_point_and_line( X, skol2 ), apart_point_and_line( X, Y ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := X
% 2.30/2.68 Y := Y
% 2.30/2.68 end
% 2.30/2.68 permutation0:
% 2.30/2.68 0 ==> 0
% 2.30/2.68 1 ==> 1
% 2.30/2.68 2 ==> 4
% 2.30/2.68 3 ==> 2
% 2.30/2.68 4 ==> 3
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 resolution: (1585) {G1,W6,D2,L2,V1,M2} { distinct_points( X, skol1 ), !
% 2.30/2.68 apart_point_and_line( X, skol3 ) }.
% 2.30/2.68 parent0[0]: (18) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol1,
% 2.30/2.68 skol3 ) }.
% 2.30/2.68 parent1[1]: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ),
% 2.30/2.68 apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 end
% 2.30/2.68 substitution1:
% 2.30/2.68 X := X
% 2.30/2.68 Y := skol3
% 2.30/2.68 Z := skol1
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 subsumption: (106) {G1,W6,D2,L2,V1,M1} R(11,18) { distinct_points( X, skol1
% 2.30/2.68 ), ! apart_point_and_line( X, skol3 ) }.
% 2.30/2.68 parent0: (1585) {G1,W6,D2,L2,V1,M2} { distinct_points( X, skol1 ), !
% 2.30/2.68 apart_point_and_line( X, skol3 ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := X
% 2.30/2.68 end
% 2.30/2.68 permutation0:
% 2.30/2.68 0 ==> 0
% 2.30/2.68 1 ==> 1
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 resolution: (1586) {G1,W9,D2,L3,V2,M3} { distinct_points( X, skol1 ),
% 2.30/2.68 distinct_points( Y, X ), ! apart_point_and_line( Y, skol3 ) }.
% 2.30/2.68 parent0[1]: (106) {G1,W6,D2,L2,V1,M1} R(11,18) { distinct_points( X, skol1
% 2.30/2.68 ), ! apart_point_and_line( X, skol3 ) }.
% 2.30/2.68 parent1[1]: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ),
% 2.30/2.68 apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := X
% 2.30/2.68 end
% 2.30/2.68 substitution1:
% 2.30/2.68 X := Y
% 2.30/2.68 Y := skol3
% 2.30/2.68 Z := X
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 subsumption: (108) {G2,W9,D2,L3,V2,M1} R(106,11) { distinct_points( X,
% 2.30/2.68 skol1 ), distinct_points( Y, X ), ! apart_point_and_line( Y, skol3 ) }.
% 2.30/2.68 parent0: (1586) {G1,W9,D2,L3,V2,M3} { distinct_points( X, skol1 ),
% 2.30/2.68 distinct_points( Y, X ), ! apart_point_and_line( Y, skol3 ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := X
% 2.30/2.68 Y := Y
% 2.30/2.68 end
% 2.30/2.68 permutation0:
% 2.30/2.68 0 ==> 0
% 2.30/2.68 1 ==> 1
% 2.30/2.68 2 ==> 2
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 resolution: (1588) {G1,W9,D2,L3,V3,M3} { distinct_lines( Y, X ), !
% 2.30/2.68 convergent_lines( Z, X ), convergent_lines( Z, Y ) }.
% 2.30/2.68 parent0[0]: (30) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 2.30/2.68 distinct_lines( X, Y ) }.
% 2.30/2.68 parent1[2]: (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ),
% 2.30/2.68 convergent_lines( X, Z ), distinct_lines( Y, Z ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := Y
% 2.30/2.68 Y := X
% 2.30/2.68 end
% 2.30/2.68 substitution1:
% 2.30/2.68 X := Z
% 2.30/2.68 Y := X
% 2.30/2.68 Z := Y
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 subsumption: (136) {G2,W9,D2,L3,V3,M1} R(13,30) { ! convergent_lines( X, Y
% 2.30/2.68 ), convergent_lines( X, Z ), distinct_lines( Z, Y ) }.
% 2.30/2.68 parent0: (1588) {G1,W9,D2,L3,V3,M3} { distinct_lines( Y, X ), !
% 2.30/2.68 convergent_lines( Z, X ), convergent_lines( Z, Y ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := Y
% 2.30/2.68 Y := Z
% 2.30/2.68 Z := X
% 2.30/2.68 end
% 2.30/2.68 permutation0:
% 2.30/2.68 0 ==> 2
% 2.30/2.68 1 ==> 0
% 2.30/2.68 2 ==> 1
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 resolution: (1589) {G1,W12,D2,L4,V3,M4} { distinct_points( X, skol1 ),
% 2.30/2.68 distinct_points( Y, X ), distinct_points( Z, Y ), ! apart_point_and_line
% 2.30/2.68 ( Z, skol3 ) }.
% 2.30/2.68 parent0[2]: (108) {G2,W9,D2,L3,V2,M1} R(106,11) { distinct_points( X, skol1
% 2.30/2.68 ), distinct_points( Y, X ), ! apart_point_and_line( Y, skol3 ) }.
% 2.30/2.68 parent1[1]: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ),
% 2.30/2.68 apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := X
% 2.30/2.68 Y := Y
% 2.30/2.68 end
% 2.30/2.68 substitution1:
% 2.30/2.68 X := Z
% 2.30/2.68 Y := skol3
% 2.30/2.68 Z := Y
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 subsumption: (235) {G3,W12,D2,L4,V3,M1} R(108,11) { distinct_points( X,
% 2.30/2.68 skol1 ), distinct_points( Y, X ), distinct_points( Z, Y ), !
% 2.30/2.68 apart_point_and_line( Z, skol3 ) }.
% 2.30/2.68 parent0: (1589) {G1,W12,D2,L4,V3,M4} { distinct_points( X, skol1 ),
% 2.30/2.68 distinct_points( Y, X ), distinct_points( Z, Y ), ! apart_point_and_line
% 2.30/2.68 ( Z, skol3 ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := X
% 2.30/2.68 Y := Y
% 2.30/2.68 Z := Z
% 2.30/2.68 end
% 2.30/2.68 permutation0:
% 2.30/2.68 0 ==> 0
% 2.30/2.68 1 ==> 1
% 2.30/2.68 2 ==> 2
% 2.30/2.68 3 ==> 3
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 factor: (1595) {G3,W9,D2,L3,V1,M3} { distinct_points( X, skol1 ),
% 2.30/2.68 distinct_points( skol1, X ), ! apart_point_and_line( X, skol3 ) }.
% 2.30/2.68 parent0[0, 2]: (235) {G3,W12,D2,L4,V3,M1} R(108,11) { distinct_points( X,
% 2.30/2.68 skol1 ), distinct_points( Y, X ), distinct_points( Z, Y ), !
% 2.30/2.68 apart_point_and_line( Z, skol3 ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := X
% 2.30/2.68 Y := skol1
% 2.30/2.68 Z := X
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 resolution: (1601) {G2,W9,D2,L3,V1,M3} { distinct_points( skol1, X ),
% 2.30/2.68 distinct_points( skol1, X ), ! apart_point_and_line( X, skol3 ) }.
% 2.30/2.68 parent0[0]: (21) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ),
% 2.30/2.68 distinct_points( X, Y ) }.
% 2.30/2.68 parent1[0]: (1595) {G3,W9,D2,L3,V1,M3} { distinct_points( X, skol1 ),
% 2.30/2.68 distinct_points( skol1, X ), ! apart_point_and_line( X, skol3 ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := skol1
% 2.30/2.68 Y := X
% 2.30/2.68 end
% 2.30/2.68 substitution1:
% 2.30/2.68 X := X
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 factor: (1603) {G2,W6,D2,L2,V1,M2} { distinct_points( skol1, X ), !
% 2.30/2.68 apart_point_and_line( X, skol3 ) }.
% 2.30/2.68 parent0[0, 1]: (1601) {G2,W9,D2,L3,V1,M3} { distinct_points( skol1, X ),
% 2.30/2.68 distinct_points( skol1, X ), ! apart_point_and_line( X, skol3 ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := X
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 subsumption: (236) {G4,W6,D2,L2,V1,M1} F(235);r(21) { distinct_points(
% 2.30/2.68 skol1, X ), ! apart_point_and_line( X, skol3 ) }.
% 2.30/2.68 parent0: (1603) {G2,W6,D2,L2,V1,M2} { distinct_points( skol1, X ), !
% 2.30/2.68 apart_point_and_line( X, skol3 ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := X
% 2.30/2.68 end
% 2.30/2.68 permutation0:
% 2.30/2.68 0 ==> 0
% 2.30/2.68 1 ==> 1
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 resolution: (1610) {G2,W15,D2,L5,V1,M5} { distinct_points( skol1, skol1 )
% 2.30/2.68 , ! distinct_points( skol1, X ), ! distinct_lines( skol2, skol3 ),
% 2.30/2.68 apart_point_and_line( X, skol2 ), apart_point_and_line( X, skol3 ) }.
% 2.30/2.68 parent0[1]: (236) {G4,W6,D2,L2,V1,M1} F(235);r(21) { distinct_points( skol1
% 2.30/2.68 , X ), ! apart_point_and_line( X, skol3 ) }.
% 2.30/2.68 parent1[4]: (75) {G1,W15,D2,L5,V2,M3} R(10,17) { ! distinct_points( skol1,
% 2.30/2.68 X ), ! distinct_lines( skol2, Y ), apart_point_and_line( X, skol2 ),
% 2.30/2.68 apart_point_and_line( X, Y ), apart_point_and_line( skol1, Y ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := skol1
% 2.30/2.68 end
% 2.30/2.68 substitution1:
% 2.30/2.68 X := X
% 2.30/2.68 Y := skol3
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 resolution: (1611) {G1,W12,D2,L4,V1,M4} { ! distinct_points( skol1, X ), !
% 2.30/2.68 distinct_lines( skol2, skol3 ), apart_point_and_line( X, skol2 ),
% 2.30/2.68 apart_point_and_line( X, skol3 ) }.
% 2.30/2.68 parent0[0]: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 2.30/2.68 parent1[0]: (1610) {G2,W15,D2,L5,V1,M5} { distinct_points( skol1, skol1 )
% 2.30/2.68 , ! distinct_points( skol1, X ), ! distinct_lines( skol2, skol3 ),
% 2.30/2.68 apart_point_and_line( X, skol2 ), apart_point_and_line( X, skol3 ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := skol1
% 2.30/2.68 end
% 2.30/2.68 substitution1:
% 2.30/2.68 X := X
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 subsumption: (686) {G5,W12,D2,L4,V1,M1} R(75,236);r(0) { ! distinct_points
% 2.30/2.68 ( skol1, X ), ! distinct_lines( skol2, skol3 ), apart_point_and_line( X,
% 2.30/2.68 skol2 ), apart_point_and_line( X, skol3 ) }.
% 2.30/2.68 parent0: (1611) {G1,W12,D2,L4,V1,M4} { ! distinct_points( skol1, X ), !
% 2.30/2.68 distinct_lines( skol2, skol3 ), apart_point_and_line( X, skol2 ),
% 2.30/2.68 apart_point_and_line( X, skol3 ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := X
% 2.30/2.68 end
% 2.30/2.68 permutation0:
% 2.30/2.68 0 ==> 0
% 2.30/2.68 1 ==> 1
% 2.30/2.68 2 ==> 2
% 2.30/2.68 3 ==> 3
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 resolution: (1613) {G1,W16,D3,L4,V1,M4} { ! convergent_lines( X, skol3 ),
% 2.30/2.68 ! distinct_points( skol1, intersection_point( X, skol3 ) ), !
% 2.30/2.68 distinct_lines( skol2, skol3 ), apart_point_and_line( intersection_point
% 2.30/2.68 ( X, skol3 ), skol2 ) }.
% 2.30/2.68 parent0[1]: (9) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 2.30/2.68 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 2.30/2.68 parent1[3]: (686) {G5,W12,D2,L4,V1,M1} R(75,236);r(0) { ! distinct_points(
% 2.30/2.68 skol1, X ), ! distinct_lines( skol2, skol3 ), apart_point_and_line( X,
% 2.30/2.68 skol2 ), apart_point_and_line( X, skol3 ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := X
% 2.30/2.68 Y := skol3
% 2.30/2.68 end
% 2.30/2.68 substitution1:
% 2.30/2.68 X := intersection_point( X, skol3 )
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 subsumption: (852) {G6,W16,D3,L4,V1,M1} R(686,9) { ! distinct_points( skol1
% 2.30/2.68 , intersection_point( X, skol3 ) ), ! distinct_lines( skol2, skol3 ), !
% 2.30/2.68 convergent_lines( X, skol3 ), apart_point_and_line( intersection_point( X
% 2.30/2.68 , skol3 ), skol2 ) }.
% 2.30/2.68 parent0: (1613) {G1,W16,D3,L4,V1,M4} { ! convergent_lines( X, skol3 ), !
% 2.30/2.68 distinct_points( skol1, intersection_point( X, skol3 ) ), !
% 2.30/2.68 distinct_lines( skol2, skol3 ), apart_point_and_line( intersection_point
% 2.30/2.68 ( X, skol3 ), skol2 ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := X
% 2.30/2.68 end
% 2.30/2.68 permutation0:
% 2.30/2.68 0 ==> 2
% 2.30/2.68 1 ==> 0
% 2.30/2.68 2 ==> 1
% 2.30/2.68 3 ==> 3
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 resolution: (1614) {G1,W14,D3,L4,V0,M4} { ! convergent_lines( skol2, skol3
% 2.30/2.68 ), ! distinct_points( skol1, intersection_point( skol2, skol3 ) ), !
% 2.30/2.68 distinct_lines( skol2, skol3 ), ! convergent_lines( skol2, skol3 ) }.
% 2.30/2.68 parent0[1]: (8) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 2.30/2.68 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 2.30/2.68 parent1[3]: (852) {G6,W16,D3,L4,V1,M1} R(686,9) { ! distinct_points( skol1
% 2.30/2.68 , intersection_point( X, skol3 ) ), ! distinct_lines( skol2, skol3 ), !
% 2.30/2.68 convergent_lines( X, skol3 ), apart_point_and_line( intersection_point( X
% 2.30/2.68 , skol3 ), skol2 ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := skol2
% 2.30/2.68 Y := skol3
% 2.30/2.68 end
% 2.30/2.68 substitution1:
% 2.30/2.68 X := skol2
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 resolution: (1616) {G1,W9,D2,L3,V0,M3} { ! convergent_lines( skol2, skol3
% 2.30/2.68 ), ! distinct_lines( skol2, skol3 ), ! convergent_lines( skol2, skol3 )
% 2.30/2.68 }.
% 2.30/2.68 parent0[1]: (1614) {G1,W14,D3,L4,V0,M4} { ! convergent_lines( skol2, skol3
% 2.30/2.68 ), ! distinct_points( skol1, intersection_point( skol2, skol3 ) ), !
% 2.30/2.68 distinct_lines( skol2, skol3 ), ! convergent_lines( skol2, skol3 ) }.
% 2.30/2.68 parent1[0]: (16) {G0,W5,D3,L1,V0,M1} I { distinct_points( skol1,
% 2.30/2.68 intersection_point( skol2, skol3 ) ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 end
% 2.30/2.68 substitution1:
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 factor: (1617) {G1,W6,D2,L2,V0,M2} { ! convergent_lines( skol2, skol3 ), !
% 2.30/2.68 distinct_lines( skol2, skol3 ) }.
% 2.30/2.68 parent0[0, 2]: (1616) {G1,W9,D2,L3,V0,M3} { ! convergent_lines( skol2,
% 2.30/2.68 skol3 ), ! distinct_lines( skol2, skol3 ), ! convergent_lines( skol2,
% 2.30/2.68 skol3 ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 subsumption: (1322) {G7,W6,D2,L2,V0,M1} R(852,8);f;r(16) { !
% 2.30/2.68 convergent_lines( skol2, skol3 ), ! distinct_lines( skol2, skol3 ) }.
% 2.30/2.68 parent0: (1617) {G1,W6,D2,L2,V0,M2} { ! convergent_lines( skol2, skol3 ),
% 2.30/2.68 ! distinct_lines( skol2, skol3 ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 end
% 2.30/2.68 permutation0:
% 2.30/2.68 0 ==> 0
% 2.30/2.68 1 ==> 1
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 resolution: (1618) {G1,W3,D2,L1,V0,M1} { ! distinct_lines( skol2, skol3 )
% 2.30/2.68 }.
% 2.30/2.68 parent0[0]: (1322) {G7,W6,D2,L2,V0,M1} R(852,8);f;r(16) { !
% 2.30/2.68 convergent_lines( skol2, skol3 ), ! distinct_lines( skol2, skol3 ) }.
% 2.30/2.68 parent1[0]: (15) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol2, skol3 )
% 2.30/2.68 }.
% 2.30/2.68 substitution0:
% 2.30/2.68 end
% 2.30/2.68 substitution1:
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 subsumption: (1323) {G8,W3,D2,L1,V0,M1} S(1322);r(15) { ! distinct_lines(
% 2.30/2.68 skol2, skol3 ) }.
% 2.30/2.68 parent0: (1618) {G1,W3,D2,L1,V0,M1} { ! distinct_lines( skol2, skol3 ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 end
% 2.30/2.68 permutation0:
% 2.30/2.68 0 ==> 0
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 resolution: (1619) {G3,W6,D2,L2,V1,M2} { ! convergent_lines( X, skol3 ),
% 2.30/2.68 convergent_lines( X, skol2 ) }.
% 2.30/2.68 parent0[0]: (1323) {G8,W3,D2,L1,V0,M1} S(1322);r(15) { ! distinct_lines(
% 2.30/2.68 skol2, skol3 ) }.
% 2.30/2.68 parent1[2]: (136) {G2,W9,D2,L3,V3,M1} R(13,30) { ! convergent_lines( X, Y )
% 2.30/2.68 , convergent_lines( X, Z ), distinct_lines( Z, Y ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 end
% 2.30/2.68 substitution1:
% 2.30/2.68 X := X
% 2.30/2.68 Y := skol3
% 2.30/2.68 Z := skol2
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 resolution: (1620) {G4,W6,D2,L2,V1,M2} { convergent_lines( X, skol2 ),
% 2.30/2.68 convergent_lines( X, skol2 ) }.
% 2.30/2.68 parent0[0]: (1619) {G3,W6,D2,L2,V1,M2} { ! convergent_lines( X, skol3 ),
% 2.30/2.68 convergent_lines( X, skol2 ) }.
% 2.30/2.68 parent1[1]: (44) {G3,W6,D2,L2,V1,M1} R(42,38) { convergent_lines( X, skol2
% 2.30/2.68 ), convergent_lines( X, skol3 ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := X
% 2.30/2.68 end
% 2.30/2.68 substitution1:
% 2.30/2.68 X := X
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 factor: (1621) {G4,W3,D2,L1,V1,M1} { convergent_lines( X, skol2 ) }.
% 2.30/2.68 parent0[0, 1]: (1620) {G4,W6,D2,L2,V1,M2} { convergent_lines( X, skol2 ),
% 2.30/2.68 convergent_lines( X, skol2 ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := X
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 subsumption: (1452) {G9,W3,D2,L1,V1,M1} R(1323,136);r(44) {
% 2.30/2.68 convergent_lines( X, skol2 ) }.
% 2.30/2.68 parent0: (1621) {G4,W3,D2,L1,V1,M1} { convergent_lines( X, skol2 ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := X
% 2.30/2.68 end
% 2.30/2.68 permutation0:
% 2.30/2.68 0 ==> 0
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 resolution: (1622) {G1,W0,D0,L0,V0,M0} { }.
% 2.30/2.68 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 2.30/2.68 parent1[0]: (1452) {G9,W3,D2,L1,V1,M1} R(1323,136);r(44) { convergent_lines
% 2.30/2.68 ( X, skol2 ) }.
% 2.30/2.68 substitution0:
% 2.30/2.68 X := skol2
% 2.30/2.68 end
% 2.30/2.68 substitution1:
% 2.30/2.68 X := skol2
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 subsumption: (1469) {G10,W0,D0,L0,V0,M0} R(1452,2) { }.
% 2.30/2.68 parent0: (1622) {G1,W0,D0,L0,V0,M0} { }.
% 2.30/2.68 substitution0:
% 2.30/2.68 end
% 2.30/2.68 permutation0:
% 2.30/2.68 end
% 2.30/2.68
% 2.30/2.68 Proof check complete!
% 2.30/2.68
% 2.30/2.68 Memory use:
% 2.30/2.68
% 2.30/2.68 space for terms: 22775
% 2.30/2.68 space for clauses: 52991
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 clauses generated: 176585
% 2.30/2.68 clauses kept: 1470
% 2.30/2.68 clauses selected: 1025
% 2.30/2.68 clauses deleted: 9
% 2.30/2.68 clauses inuse deleted: 0
% 2.30/2.68
% 2.30/2.68 subsentry: 191902
% 2.30/2.68 literals s-matched: 122235
% 2.30/2.68 literals matched: 122200
% 2.30/2.68 full subsumption: 75865
% 2.30/2.68
% 2.30/2.68 checksum: -1741984083
% 2.30/2.68
% 2.30/2.68
% 2.30/2.68 Bliksem ended
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