TSTP Solution File: GEO172+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO172+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n022.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 02:52:13 EDT 2022
% Result : Theorem 2.16s 2.50s
% Output : Refutation 2.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO172+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : bliksem %s
% 0.14/0.34 % Computer : n022.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % DateTime : Sat Jun 18 01:26:17 EDT 2022
% 0.14/0.34 % CPUTime :
% 2.16/2.50 *** allocated 10000 integers for termspace/termends
% 2.16/2.50 *** allocated 10000 integers for clauses
% 2.16/2.50 *** allocated 10000 integers for justifications
% 2.16/2.50 Bliksem 1.12
% 2.16/2.50
% 2.16/2.50
% 2.16/2.50 Automatic Strategy Selection
% 2.16/2.50
% 2.16/2.50
% 2.16/2.50 Clauses:
% 2.16/2.50
% 2.16/2.50 { ! distinct_points( X, X ) }.
% 2.16/2.50 { ! distinct_lines( X, X ) }.
% 2.16/2.50 { ! convergent_lines( X, X ) }.
% 2.16/2.50 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 2.16/2.50 ) }.
% 2.16/2.50 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 2.16/2.50 }.
% 2.16/2.50 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 2.16/2.50 , Z ) }.
% 2.16/2.50 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 2.16/2.50 , Y ) ) }.
% 2.16/2.50 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 2.16/2.50 , Y ) ) }.
% 2.16/2.50 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 2.16/2.50 , Y ), X ) }.
% 2.16/2.50 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 2.16/2.50 , Y ), Y ) }.
% 2.16/2.50 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 2.16/2.50 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 2.16/2.50 apart_point_and_line( Y, T ) }.
% 2.16/2.50 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 2.16/2.50 apart_point_and_line( Z, Y ) }.
% 2.16/2.50 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 2.16/2.50 apart_point_and_line( X, Z ) }.
% 2.16/2.50 { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X,
% 2.16/2.50 Z ) }.
% 2.16/2.50 { convergent_lines( skol1, skol2 ) }.
% 2.16/2.50 { ! apart_point_and_line( skol3, skol1 ) }.
% 2.16/2.50 { ! apart_point_and_line( skol3, skol2 ) }.
% 2.16/2.50 { distinct_points( skol3, intersection_point( skol1, skol2 ) ) }.
% 2.16/2.50
% 2.16/2.50 percentage equality = 0.000000, percentage horn = 0.611111
% 2.16/2.50 This a non-horn, non-equality problem
% 2.16/2.50
% 2.16/2.50
% 2.16/2.50 Options Used:
% 2.16/2.50
% 2.16/2.50 useres = 1
% 2.16/2.50 useparamod = 0
% 2.16/2.50 useeqrefl = 0
% 2.16/2.50 useeqfact = 0
% 2.16/2.50 usefactor = 1
% 2.16/2.50 usesimpsplitting = 0
% 2.16/2.50 usesimpdemod = 0
% 2.16/2.50 usesimpres = 3
% 2.16/2.50
% 2.16/2.50 resimpinuse = 1000
% 2.16/2.50 resimpclauses = 20000
% 2.16/2.50 substype = standard
% 2.16/2.50 backwardsubs = 1
% 2.16/2.50 selectoldest = 5
% 2.16/2.50
% 2.16/2.50 litorderings [0] = split
% 2.16/2.50 litorderings [1] = liftord
% 2.16/2.50
% 2.16/2.50 termordering = none
% 2.16/2.50
% 2.16/2.50 litapriori = 1
% 2.16/2.50 termapriori = 0
% 2.16/2.50 litaposteriori = 0
% 2.16/2.50 termaposteriori = 0
% 2.16/2.50 demodaposteriori = 0
% 2.16/2.50 ordereqreflfact = 0
% 2.16/2.50
% 2.16/2.50 litselect = none
% 2.16/2.50
% 2.16/2.50 maxweight = 15
% 2.16/2.50 maxdepth = 30000
% 2.16/2.50 maxlength = 115
% 2.16/2.50 maxnrvars = 195
% 2.16/2.50 excuselevel = 1
% 2.16/2.50 increasemaxweight = 1
% 2.16/2.50
% 2.16/2.50 maxselected = 10000000
% 2.16/2.50 maxnrclauses = 10000000
% 2.16/2.50
% 2.16/2.50 showgenerated = 0
% 2.16/2.50 showkept = 0
% 2.16/2.50 showselected = 0
% 2.16/2.50 showdeleted = 0
% 2.16/2.50 showresimp = 1
% 2.16/2.50 showstatus = 2000
% 2.16/2.50
% 2.16/2.50 prologoutput = 0
% 2.16/2.50 nrgoals = 5000000
% 2.16/2.50 totalproof = 1
% 2.16/2.50
% 2.16/2.50 Symbols occurring in the translation:
% 2.16/2.50
% 2.16/2.50 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 2.16/2.50 . [1, 2] (w:1, o:19, a:1, s:1, b:0),
% 2.16/2.50 ! [4, 1] (w:0, o:14, a:1, s:1, b:0),
% 2.16/2.50 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.16/2.50 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.16/2.50 distinct_points [36, 2] (w:1, o:44, a:1, s:1, b:0),
% 2.16/2.50 distinct_lines [37, 2] (w:1, o:45, a:1, s:1, b:0),
% 2.16/2.50 convergent_lines [38, 2] (w:1, o:43, a:1, s:1, b:0),
% 2.16/2.50 line_connecting [41, 2] (w:1, o:46, a:1, s:1, b:0),
% 2.16/2.50 apart_point_and_line [42, 2] (w:1, o:47, a:1, s:1, b:0),
% 2.16/2.50 intersection_point [43, 2] (w:1, o:48, a:1, s:1, b:0),
% 2.16/2.50 skol1 [46, 0] (w:1, o:11, a:1, s:1, b:0),
% 2.16/2.50 skol2 [47, 0] (w:1, o:12, a:1, s:1, b:0),
% 2.16/2.50 skol3 [48, 0] (w:1, o:13, a:1, s:1, b:0).
% 2.16/2.50
% 2.16/2.50
% 2.16/2.50 Starting Search:
% 2.16/2.50
% 2.16/2.50 *** allocated 15000 integers for clauses
% 2.16/2.50 *** allocated 22500 integers for clauses
% 2.16/2.50 *** allocated 33750 integers for clauses
% 2.16/2.50 *** allocated 15000 integers for termspace/termends
% 2.16/2.50 Resimplifying inuse:
% 2.16/2.50 Done
% 2.16/2.50
% 2.16/2.50 Failed to find proof!
% 2.16/2.50 maxweight = 15
% 2.16/2.50 maxnrclauses = 10000000
% 2.16/2.50 Generated: 128451
% 2.16/2.50 Kept: 737
% 2.16/2.50
% 2.16/2.50
% 2.16/2.50 The strategy used was not complete!
% 2.16/2.50
% 2.16/2.50 Increased maxweight to 16
% 2.16/2.50
% 2.16/2.50 Starting Search:
% 2.16/2.50
% 2.16/2.50 *** allocated 50625 integers for clauses
% 2.16/2.50 *** allocated 22500 integers for termspace/termends
% 2.16/2.50 Resimplifying inuse:
% 2.16/2.50 Done
% 2.16/2.50
% 2.16/2.50 *** allocated 75937 integers for clauses
% 2.16/2.50 *** allocated 33750 integers for termspace/termends
% 2.16/2.50
% 2.16/2.50 Bliksems!, er is een bewijs:
% 2.16/2.50 % SZS status Theorem
% 2.16/2.50 % SZS output start Refutation
% 2.16/2.50
% 2.16/2.50 (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 2.16/2.51 (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 2.16/2.51 (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 2.16/2.51 (3) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ), distinct_points( Y, Z
% 2.16/2.51 ), ! distinct_points( X, Y ) }.
% 2.16/2.51 (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 2.16/2.51 , ! distinct_lines( X, Y ) }.
% 2.16/2.51 (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), convergent_lines( Y,
% 2.16/2.51 Z ), ! convergent_lines( X, Y ) }.
% 2.16/2.51 (8) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 2.16/2.51 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 2.16/2.51 (9) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 2.16/2.51 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 2.16/2.51 (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! distinct_lines(
% 2.16/2.51 Z, T ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 2.16/2.51 apart_point_and_line( Y, T ), apart_point_and_line( X, Z ) }.
% 2.16/2.51 (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), apart_point_and_line
% 2.16/2.51 ( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 2.16/2.51 (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ), convergent_lines(
% 2.16/2.51 X, Z ), distinct_lines( Y, Z ) }.
% 2.16/2.51 (14) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 ) }.
% 2.16/2.51 (15) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol3, skol1 ) }.
% 2.16/2.51 (16) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol3, skol2 ) }.
% 2.16/2.51 (17) {G0,W5,D3,L1,V0,M1} I { distinct_points( skol3, intersection_point(
% 2.16/2.51 skol1, skol2 ) ) }.
% 2.16/2.51 (20) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ),
% 2.16/2.51 distinct_points( X, Y ) }.
% 2.16/2.51 (27) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 2.16/2.51 ( X, Y ) }.
% 2.16/2.51 (32) {G1,W6,D2,L2,V1,M1} R(5,14) { convergent_lines( skol1, X ),
% 2.16/2.51 convergent_lines( skol2, X ) }.
% 2.16/2.51 (33) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 2.16/2.51 convergent_lines( X, Y ) }.
% 2.16/2.51 (37) {G2,W6,D2,L2,V1,M2} R(32,33) { convergent_lines( X, skol2 ),
% 2.16/2.51 convergent_lines( skol1, X ) }.
% 2.16/2.51 (39) {G3,W6,D2,L2,V1,M1} R(37,33) { convergent_lines( X, skol1 ),
% 2.16/2.51 convergent_lines( X, skol2 ) }.
% 2.16/2.51 (67) {G1,W15,D2,L5,V2,M3} R(10,15) { ! distinct_points( skol3, X ), !
% 2.16/2.51 distinct_lines( skol1, Y ), apart_point_and_line( X, skol1 ),
% 2.16/2.51 apart_point_and_line( X, Y ), apart_point_and_line( skol3, Y ) }.
% 2.16/2.51 (98) {G1,W6,D2,L2,V1,M1} R(11,16) { distinct_points( X, skol3 ), !
% 2.16/2.51 apart_point_and_line( X, skol2 ) }.
% 2.16/2.51 (100) {G2,W9,D2,L3,V2,M1} R(98,11) { distinct_points( X, skol3 ),
% 2.16/2.51 distinct_points( Y, X ), ! apart_point_and_line( Y, skol2 ) }.
% 2.16/2.51 (127) {G2,W9,D2,L3,V3,M1} R(13,27) { ! convergent_lines( X, Y ),
% 2.16/2.51 convergent_lines( X, Z ), distinct_lines( Z, Y ) }.
% 2.16/2.51 (189) {G3,W12,D2,L4,V3,M1} R(100,11) { distinct_points( X, skol3 ),
% 2.16/2.51 distinct_points( Y, X ), distinct_points( Z, Y ), ! apart_point_and_line
% 2.16/2.51 ( Z, skol2 ) }.
% 2.16/2.51 (190) {G4,W6,D2,L2,V1,M1} F(189);r(20) { distinct_points( skol3, X ), !
% 2.16/2.51 apart_point_and_line( X, skol2 ) }.
% 2.16/2.51 (624) {G5,W12,D2,L4,V1,M1} R(67,190);r(0) { ! distinct_points( skol3, X ),
% 2.16/2.51 ! distinct_lines( skol1, skol2 ), apart_point_and_line( X, skol1 ),
% 2.16/2.51 apart_point_and_line( X, skol2 ) }.
% 2.16/2.51 (790) {G6,W16,D3,L4,V1,M1} R(624,9) { ! distinct_points( skol3,
% 2.16/2.51 intersection_point( X, skol2 ) ), ! distinct_lines( skol1, skol2 ), !
% 2.16/2.51 convergent_lines( X, skol2 ), apart_point_and_line( intersection_point( X
% 2.16/2.51 , skol2 ), skol1 ) }.
% 2.16/2.51 (1292) {G7,W6,D2,L2,V0,M1} R(790,8);f;r(17) { ! convergent_lines( skol1,
% 2.16/2.51 skol2 ), ! distinct_lines( skol1, skol2 ) }.
% 2.16/2.51 (1293) {G8,W3,D2,L1,V0,M1} S(1292);r(14) { ! distinct_lines( skol1, skol2 )
% 2.16/2.51 }.
% 2.16/2.51 (1424) {G9,W3,D2,L1,V1,M1} R(1293,127);r(39) { convergent_lines( X, skol1 )
% 2.16/2.51 }.
% 2.16/2.51 (1443) {G10,W0,D0,L0,V0,M0} R(1424,2) { }.
% 2.16/2.51
% 2.16/2.51
% 2.16/2.51 % SZS output end Refutation
% 2.16/2.51 found a proof!
% 2.16/2.51
% 2.16/2.51
% 2.16/2.51 Unprocessed initial clauses:
% 2.16/2.51
% 2.16/2.51 (1445) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 2.16/2.51 (1446) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 2.16/2.51 (1447) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 2.16/2.51 (1448) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 2.16/2.51 , Z ), distinct_points( Y, Z ) }.
% 2.16/2.51 (1449) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X,
% 2.16/2.51 Z ), distinct_lines( Y, Z ) }.
% 2.16/2.51 (1450) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines
% 2.16/2.51 ( X, Z ), convergent_lines( Y, Z ) }.
% 2.16/2.51 (1451) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 2.16/2.51 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 2.16/2.51 (1452) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 2.16/2.51 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 2.16/2.51 (1453) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 2.16/2.51 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 2.16/2.51 (1454) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 2.16/2.51 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 2.16/2.51 (1455) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines
% 2.16/2.51 ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 2.16/2.51 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 2.16/2.51 (1456) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 2.16/2.51 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 2.16/2.51 (1457) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 2.16/2.51 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 2.16/2.51 (1458) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), distinct_lines( Y
% 2.16/2.51 , Z ), convergent_lines( X, Z ) }.
% 2.16/2.51 (1459) {G0,W3,D2,L1,V0,M1} { convergent_lines( skol1, skol2 ) }.
% 2.16/2.51 (1460) {G0,W3,D2,L1,V0,M1} { ! apart_point_and_line( skol3, skol1 ) }.
% 2.16/2.51 (1461) {G0,W3,D2,L1,V0,M1} { ! apart_point_and_line( skol3, skol2 ) }.
% 2.16/2.51 (1462) {G0,W5,D3,L1,V0,M1} { distinct_points( skol3, intersection_point(
% 2.16/2.51 skol1, skol2 ) ) }.
% 2.16/2.51
% 2.16/2.51
% 2.16/2.51 Total Proof:
% 2.16/2.51
% 2.16/2.51 subsumption: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 2.16/2.51 parent0: (1445) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := X
% 2.16/2.51 end
% 2.16/2.51 permutation0:
% 2.16/2.51 0 ==> 0
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 2.16/2.51 parent0: (1446) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := X
% 2.16/2.51 end
% 2.16/2.51 permutation0:
% 2.16/2.51 0 ==> 0
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 subsumption: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 2.16/2.51 parent0: (1447) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := X
% 2.16/2.51 end
% 2.16/2.51 permutation0:
% 2.16/2.51 0 ==> 0
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 subsumption: (3) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ),
% 2.16/2.51 distinct_points( Y, Z ), ! distinct_points( X, Y ) }.
% 2.16/2.51 parent0: (1448) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ),
% 2.16/2.51 distinct_points( X, Z ), distinct_points( Y, Z ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := X
% 2.16/2.51 Y := Y
% 2.16/2.51 Z := Z
% 2.16/2.51 end
% 2.16/2.51 permutation0:
% 2.16/2.51 0 ==> 2
% 2.16/2.51 1 ==> 0
% 2.16/2.51 2 ==> 1
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 2.16/2.51 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 2.16/2.51 parent0: (1449) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ),
% 2.16/2.51 distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := X
% 2.16/2.51 Y := Y
% 2.16/2.51 Z := Z
% 2.16/2.51 end
% 2.16/2.51 permutation0:
% 2.16/2.51 0 ==> 2
% 2.16/2.51 1 ==> 0
% 2.16/2.51 2 ==> 1
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 subsumption: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 2.16/2.51 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 2.16/2.51 parent0: (1450) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 2.16/2.51 convergent_lines( X, Z ), convergent_lines( Y, Z ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := X
% 2.16/2.51 Y := Y
% 2.16/2.51 Z := Z
% 2.16/2.51 end
% 2.16/2.51 permutation0:
% 2.16/2.51 0 ==> 2
% 2.16/2.51 1 ==> 0
% 2.16/2.51 2 ==> 1
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 subsumption: (8) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 2.16/2.51 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 2.16/2.51 parent0: (1453) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 2.16/2.51 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := X
% 2.16/2.51 Y := Y
% 2.16/2.51 end
% 2.16/2.51 permutation0:
% 2.16/2.51 0 ==> 0
% 2.16/2.51 1 ==> 1
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 subsumption: (9) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 2.16/2.51 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 2.16/2.51 parent0: (1454) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 2.16/2.51 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := X
% 2.16/2.51 Y := Y
% 2.16/2.51 end
% 2.16/2.51 permutation0:
% 2.16/2.51 0 ==> 0
% 2.16/2.51 1 ==> 1
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 subsumption: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), !
% 2.16/2.51 distinct_lines( Z, T ), apart_point_and_line( X, T ),
% 2.16/2.51 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ),
% 2.16/2.51 apart_point_and_line( X, Z ) }.
% 2.16/2.51 parent0: (1455) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), !
% 2.16/2.51 distinct_lines( Z, T ), apart_point_and_line( X, Z ),
% 2.16/2.51 apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 2.16/2.51 apart_point_and_line( Y, T ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := X
% 2.16/2.51 Y := Y
% 2.16/2.51 Z := Z
% 2.16/2.51 T := T
% 2.16/2.51 end
% 2.16/2.51 permutation0:
% 2.16/2.51 0 ==> 0
% 2.16/2.51 1 ==> 1
% 2.16/2.51 2 ==> 5
% 2.16/2.51 3 ==> 2
% 2.16/2.51 4 ==> 3
% 2.16/2.51 5 ==> 4
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 subsumption: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ),
% 2.16/2.51 apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 2.16/2.51 parent0: (1456) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 2.16/2.51 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := X
% 2.16/2.51 Y := Y
% 2.16/2.51 Z := Z
% 2.16/2.51 end
% 2.16/2.51 permutation0:
% 2.16/2.51 0 ==> 2
% 2.16/2.51 1 ==> 0
% 2.16/2.51 2 ==> 1
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 subsumption: (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ),
% 2.16/2.51 convergent_lines( X, Z ), distinct_lines( Y, Z ) }.
% 2.16/2.51 parent0: (1458) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 2.16/2.51 distinct_lines( Y, Z ), convergent_lines( X, Z ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := X
% 2.16/2.51 Y := Y
% 2.16/2.51 Z := Z
% 2.16/2.51 end
% 2.16/2.51 permutation0:
% 2.16/2.51 0 ==> 0
% 2.16/2.51 1 ==> 2
% 2.16/2.51 2 ==> 1
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 subsumption: (14) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 )
% 2.16/2.51 }.
% 2.16/2.51 parent0: (1459) {G0,W3,D2,L1,V0,M1} { convergent_lines( skol1, skol2 ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 end
% 2.16/2.51 permutation0:
% 2.16/2.51 0 ==> 0
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 subsumption: (15) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol3,
% 2.16/2.51 skol1 ) }.
% 2.16/2.51 parent0: (1460) {G0,W3,D2,L1,V0,M1} { ! apart_point_and_line( skol3, skol1
% 2.16/2.51 ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 end
% 2.16/2.51 permutation0:
% 2.16/2.51 0 ==> 0
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 subsumption: (16) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol3,
% 2.16/2.51 skol2 ) }.
% 2.16/2.51 parent0: (1461) {G0,W3,D2,L1,V0,M1} { ! apart_point_and_line( skol3, skol2
% 2.16/2.51 ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 end
% 2.16/2.51 permutation0:
% 2.16/2.51 0 ==> 0
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 subsumption: (17) {G0,W5,D3,L1,V0,M1} I { distinct_points( skol3,
% 2.16/2.51 intersection_point( skol1, skol2 ) ) }.
% 2.16/2.51 parent0: (1462) {G0,W5,D3,L1,V0,M1} { distinct_points( skol3,
% 2.16/2.51 intersection_point( skol1, skol2 ) ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 end
% 2.16/2.51 permutation0:
% 2.16/2.51 0 ==> 0
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 resolution: (1538) {G1,W6,D2,L2,V2,M2} { distinct_points( Y, X ), !
% 2.16/2.51 distinct_points( X, Y ) }.
% 2.16/2.51 parent0[0]: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 2.16/2.51 parent1[0]: (3) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ),
% 2.16/2.51 distinct_points( Y, Z ), ! distinct_points( X, Y ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := X
% 2.16/2.51 end
% 2.16/2.51 substitution1:
% 2.16/2.51 X := X
% 2.16/2.51 Y := Y
% 2.16/2.51 Z := X
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 subsumption: (20) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ),
% 2.16/2.51 distinct_points( X, Y ) }.
% 2.16/2.51 parent0: (1538) {G1,W6,D2,L2,V2,M2} { distinct_points( Y, X ), !
% 2.16/2.51 distinct_points( X, Y ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := Y
% 2.16/2.51 Y := X
% 2.16/2.51 end
% 2.16/2.51 permutation0:
% 2.16/2.51 0 ==> 1
% 2.16/2.51 1 ==> 0
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 resolution: (1540) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 2.16/2.51 distinct_lines( X, Y ) }.
% 2.16/2.51 parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 2.16/2.51 parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 2.16/2.51 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := X
% 2.16/2.51 end
% 2.16/2.51 substitution1:
% 2.16/2.51 X := X
% 2.16/2.51 Y := Y
% 2.16/2.51 Z := X
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 subsumption: (27) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 2.16/2.51 distinct_lines( X, Y ) }.
% 2.16/2.51 parent0: (1540) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 2.16/2.51 distinct_lines( X, Y ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := Y
% 2.16/2.51 Y := X
% 2.16/2.51 end
% 2.16/2.51 permutation0:
% 2.16/2.51 0 ==> 1
% 2.16/2.51 1 ==> 0
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 resolution: (1542) {G1,W6,D2,L2,V1,M2} { convergent_lines( skol1, X ),
% 2.16/2.51 convergent_lines( skol2, X ) }.
% 2.16/2.51 parent0[2]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 2.16/2.51 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 2.16/2.51 parent1[0]: (14) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 )
% 2.16/2.51 }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := skol1
% 2.16/2.51 Y := skol2
% 2.16/2.51 Z := X
% 2.16/2.51 end
% 2.16/2.51 substitution1:
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 subsumption: (32) {G1,W6,D2,L2,V1,M1} R(5,14) { convergent_lines( skol1, X
% 2.16/2.51 ), convergent_lines( skol2, X ) }.
% 2.16/2.51 parent0: (1542) {G1,W6,D2,L2,V1,M2} { convergent_lines( skol1, X ),
% 2.16/2.51 convergent_lines( skol2, X ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := X
% 2.16/2.51 end
% 2.16/2.51 permutation0:
% 2.16/2.51 0 ==> 0
% 2.16/2.51 1 ==> 1
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 resolution: (1543) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 2.16/2.51 convergent_lines( X, Y ) }.
% 2.16/2.51 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 2.16/2.51 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 2.16/2.51 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := X
% 2.16/2.51 end
% 2.16/2.51 substitution1:
% 2.16/2.51 X := X
% 2.16/2.51 Y := Y
% 2.16/2.51 Z := X
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 subsumption: (33) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 2.16/2.51 convergent_lines( X, Y ) }.
% 2.16/2.51 parent0: (1543) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 2.16/2.51 convergent_lines( X, Y ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := Y
% 2.16/2.51 Y := X
% 2.16/2.51 end
% 2.16/2.51 permutation0:
% 2.16/2.51 0 ==> 1
% 2.16/2.51 1 ==> 0
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 resolution: (1546) {G2,W6,D2,L2,V1,M2} { convergent_lines( X, skol2 ),
% 2.16/2.51 convergent_lines( skol1, X ) }.
% 2.16/2.51 parent0[0]: (33) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 2.16/2.51 convergent_lines( X, Y ) }.
% 2.16/2.51 parent1[1]: (32) {G1,W6,D2,L2,V1,M1} R(5,14) { convergent_lines( skol1, X )
% 2.16/2.51 , convergent_lines( skol2, X ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := X
% 2.16/2.51 Y := skol2
% 2.16/2.51 end
% 2.16/2.51 substitution1:
% 2.16/2.51 X := X
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 subsumption: (37) {G2,W6,D2,L2,V1,M2} R(32,33) { convergent_lines( X, skol2
% 2.16/2.51 ), convergent_lines( skol1, X ) }.
% 2.16/2.51 parent0: (1546) {G2,W6,D2,L2,V1,M2} { convergent_lines( X, skol2 ),
% 2.16/2.51 convergent_lines( skol1, X ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := X
% 2.16/2.51 end
% 2.16/2.51 permutation0:
% 2.16/2.51 0 ==> 0
% 2.16/2.51 1 ==> 1
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 resolution: (1548) {G2,W6,D2,L2,V1,M2} { convergent_lines( X, skol1 ),
% 2.16/2.51 convergent_lines( X, skol2 ) }.
% 2.16/2.51 parent0[0]: (33) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 2.16/2.51 convergent_lines( X, Y ) }.
% 2.16/2.51 parent1[1]: (37) {G2,W6,D2,L2,V1,M2} R(32,33) { convergent_lines( X, skol2
% 2.16/2.51 ), convergent_lines( skol1, X ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := X
% 2.16/2.51 Y := skol1
% 2.16/2.51 end
% 2.16/2.51 substitution1:
% 2.16/2.51 X := X
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 subsumption: (39) {G3,W6,D2,L2,V1,M1} R(37,33) { convergent_lines( X, skol1
% 2.16/2.51 ), convergent_lines( X, skol2 ) }.
% 2.16/2.51 parent0: (1548) {G2,W6,D2,L2,V1,M2} { convergent_lines( X, skol1 ),
% 2.16/2.51 convergent_lines( X, skol2 ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := X
% 2.16/2.51 end
% 2.16/2.51 permutation0:
% 2.16/2.51 0 ==> 0
% 2.16/2.51 1 ==> 1
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 resolution: (1552) {G1,W15,D2,L5,V2,M5} { ! distinct_points( skol3, X ), !
% 2.16/2.51 distinct_lines( skol1, Y ), apart_point_and_line( skol3, Y ),
% 2.16/2.51 apart_point_and_line( X, skol1 ), apart_point_and_line( X, Y ) }.
% 2.16/2.51 parent0[0]: (15) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol3,
% 2.16/2.51 skol1 ) }.
% 2.16/2.51 parent1[5]: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), !
% 2.16/2.51 distinct_lines( Z, T ), apart_point_and_line( X, T ),
% 2.16/2.51 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ),
% 2.16/2.51 apart_point_and_line( X, Z ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 end
% 2.16/2.51 substitution1:
% 2.16/2.51 X := skol3
% 2.16/2.51 Y := X
% 2.16/2.51 Z := skol1
% 2.16/2.51 T := Y
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 subsumption: (67) {G1,W15,D2,L5,V2,M3} R(10,15) { ! distinct_points( skol3
% 2.16/2.51 , X ), ! distinct_lines( skol1, Y ), apart_point_and_line( X, skol1 ),
% 2.16/2.51 apart_point_and_line( X, Y ), apart_point_and_line( skol3, Y ) }.
% 2.16/2.51 parent0: (1552) {G1,W15,D2,L5,V2,M5} { ! distinct_points( skol3, X ), !
% 2.16/2.51 distinct_lines( skol1, Y ), apart_point_and_line( skol3, Y ),
% 2.16/2.51 apart_point_and_line( X, skol1 ), apart_point_and_line( X, Y ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := X
% 2.16/2.51 Y := Y
% 2.16/2.51 end
% 2.16/2.51 permutation0:
% 2.16/2.51 0 ==> 0
% 2.16/2.51 1 ==> 1
% 2.16/2.51 2 ==> 4
% 2.16/2.51 3 ==> 2
% 2.16/2.51 4 ==> 3
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 resolution: (1558) {G1,W6,D2,L2,V1,M2} { distinct_points( X, skol3 ), !
% 2.16/2.51 apart_point_and_line( X, skol2 ) }.
% 2.16/2.51 parent0[0]: (16) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol3,
% 2.16/2.51 skol2 ) }.
% 2.16/2.51 parent1[1]: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ),
% 2.16/2.51 apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 end
% 2.16/2.51 substitution1:
% 2.16/2.51 X := X
% 2.16/2.51 Y := skol2
% 2.16/2.51 Z := skol3
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 subsumption: (98) {G1,W6,D2,L2,V1,M1} R(11,16) { distinct_points( X, skol3
% 2.16/2.51 ), ! apart_point_and_line( X, skol2 ) }.
% 2.16/2.51 parent0: (1558) {G1,W6,D2,L2,V1,M2} { distinct_points( X, skol3 ), !
% 2.16/2.51 apart_point_and_line( X, skol2 ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := X
% 2.16/2.51 end
% 2.16/2.51 permutation0:
% 2.16/2.51 0 ==> 0
% 2.16/2.51 1 ==> 1
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 resolution: (1559) {G1,W9,D2,L3,V2,M3} { distinct_points( X, skol3 ),
% 2.16/2.51 distinct_points( Y, X ), ! apart_point_and_line( Y, skol2 ) }.
% 2.16/2.51 parent0[1]: (98) {G1,W6,D2,L2,V1,M1} R(11,16) { distinct_points( X, skol3 )
% 2.16/2.51 , ! apart_point_and_line( X, skol2 ) }.
% 2.16/2.51 parent1[1]: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ),
% 2.16/2.51 apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := X
% 2.16/2.51 end
% 2.16/2.51 substitution1:
% 2.16/2.51 X := Y
% 2.16/2.51 Y := skol2
% 2.16/2.51 Z := X
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 subsumption: (100) {G2,W9,D2,L3,V2,M1} R(98,11) { distinct_points( X, skol3
% 2.16/2.51 ), distinct_points( Y, X ), ! apart_point_and_line( Y, skol2 ) }.
% 2.16/2.51 parent0: (1559) {G1,W9,D2,L3,V2,M3} { distinct_points( X, skol3 ),
% 2.16/2.51 distinct_points( Y, X ), ! apart_point_and_line( Y, skol2 ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := X
% 2.16/2.51 Y := Y
% 2.16/2.51 end
% 2.16/2.51 permutation0:
% 2.16/2.51 0 ==> 0
% 2.16/2.51 1 ==> 1
% 2.16/2.51 2 ==> 2
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 resolution: (1561) {G1,W9,D2,L3,V3,M3} { distinct_lines( Y, X ), !
% 2.16/2.51 convergent_lines( Z, X ), convergent_lines( Z, Y ) }.
% 2.16/2.51 parent0[0]: (27) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 2.16/2.51 distinct_lines( X, Y ) }.
% 2.16/2.51 parent1[2]: (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ),
% 2.16/2.51 convergent_lines( X, Z ), distinct_lines( Y, Z ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := Y
% 2.16/2.51 Y := X
% 2.16/2.51 end
% 2.16/2.51 substitution1:
% 2.16/2.51 X := Z
% 2.16/2.51 Y := X
% 2.16/2.51 Z := Y
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 subsumption: (127) {G2,W9,D2,L3,V3,M1} R(13,27) { ! convergent_lines( X, Y
% 2.16/2.51 ), convergent_lines( X, Z ), distinct_lines( Z, Y ) }.
% 2.16/2.51 parent0: (1561) {G1,W9,D2,L3,V3,M3} { distinct_lines( Y, X ), !
% 2.16/2.51 convergent_lines( Z, X ), convergent_lines( Z, Y ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := Y
% 2.16/2.51 Y := Z
% 2.16/2.51 Z := X
% 2.16/2.51 end
% 2.16/2.51 permutation0:
% 2.16/2.51 0 ==> 2
% 2.16/2.51 1 ==> 0
% 2.16/2.51 2 ==> 1
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 resolution: (1562) {G1,W12,D2,L4,V3,M4} { distinct_points( X, skol3 ),
% 2.16/2.51 distinct_points( Y, X ), distinct_points( Z, Y ), ! apart_point_and_line
% 2.16/2.51 ( Z, skol2 ) }.
% 2.16/2.51 parent0[2]: (100) {G2,W9,D2,L3,V2,M1} R(98,11) { distinct_points( X, skol3
% 2.16/2.51 ), distinct_points( Y, X ), ! apart_point_and_line( Y, skol2 ) }.
% 2.16/2.51 parent1[1]: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ),
% 2.16/2.51 apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := X
% 2.16/2.51 Y := Y
% 2.16/2.51 end
% 2.16/2.51 substitution1:
% 2.16/2.51 X := Z
% 2.16/2.51 Y := skol2
% 2.16/2.51 Z := Y
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 subsumption: (189) {G3,W12,D2,L4,V3,M1} R(100,11) { distinct_points( X,
% 2.16/2.51 skol3 ), distinct_points( Y, X ), distinct_points( Z, Y ), !
% 2.16/2.51 apart_point_and_line( Z, skol2 ) }.
% 2.16/2.51 parent0: (1562) {G1,W12,D2,L4,V3,M4} { distinct_points( X, skol3 ),
% 2.16/2.51 distinct_points( Y, X ), distinct_points( Z, Y ), ! apart_point_and_line
% 2.16/2.51 ( Z, skol2 ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := X
% 2.16/2.51 Y := Y
% 2.16/2.51 Z := Z
% 2.16/2.51 end
% 2.16/2.51 permutation0:
% 2.16/2.51 0 ==> 0
% 2.16/2.51 1 ==> 1
% 2.16/2.51 2 ==> 2
% 2.16/2.51 3 ==> 3
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 factor: (1568) {G3,W9,D2,L3,V1,M3} { distinct_points( X, skol3 ),
% 2.16/2.51 distinct_points( skol3, X ), ! apart_point_and_line( X, skol2 ) }.
% 2.16/2.51 parent0[0, 2]: (189) {G3,W12,D2,L4,V3,M1} R(100,11) { distinct_points( X,
% 2.16/2.51 skol3 ), distinct_points( Y, X ), distinct_points( Z, Y ), !
% 2.16/2.51 apart_point_and_line( Z, skol2 ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := X
% 2.16/2.51 Y := skol3
% 2.16/2.51 Z := X
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 resolution: (1574) {G2,W9,D2,L3,V1,M3} { distinct_points( skol3, X ),
% 2.16/2.51 distinct_points( skol3, X ), ! apart_point_and_line( X, skol2 ) }.
% 2.16/2.51 parent0[0]: (20) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ),
% 2.16/2.51 distinct_points( X, Y ) }.
% 2.16/2.51 parent1[0]: (1568) {G3,W9,D2,L3,V1,M3} { distinct_points( X, skol3 ),
% 2.16/2.51 distinct_points( skol3, X ), ! apart_point_and_line( X, skol2 ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := skol3
% 2.16/2.51 Y := X
% 2.16/2.51 end
% 2.16/2.51 substitution1:
% 2.16/2.51 X := X
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 factor: (1576) {G2,W6,D2,L2,V1,M2} { distinct_points( skol3, X ), !
% 2.16/2.51 apart_point_and_line( X, skol2 ) }.
% 2.16/2.51 parent0[0, 1]: (1574) {G2,W9,D2,L3,V1,M3} { distinct_points( skol3, X ),
% 2.16/2.51 distinct_points( skol3, X ), ! apart_point_and_line( X, skol2 ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := X
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 subsumption: (190) {G4,W6,D2,L2,V1,M1} F(189);r(20) { distinct_points(
% 2.16/2.51 skol3, X ), ! apart_point_and_line( X, skol2 ) }.
% 2.16/2.51 parent0: (1576) {G2,W6,D2,L2,V1,M2} { distinct_points( skol3, X ), !
% 2.16/2.51 apart_point_and_line( X, skol2 ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := X
% 2.16/2.51 end
% 2.16/2.51 permutation0:
% 2.16/2.51 0 ==> 0
% 2.16/2.51 1 ==> 1
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 resolution: (1583) {G2,W15,D2,L5,V1,M5} { distinct_points( skol3, skol3 )
% 2.16/2.51 , ! distinct_points( skol3, X ), ! distinct_lines( skol1, skol2 ),
% 2.16/2.51 apart_point_and_line( X, skol1 ), apart_point_and_line( X, skol2 ) }.
% 2.16/2.51 parent0[1]: (190) {G4,W6,D2,L2,V1,M1} F(189);r(20) { distinct_points( skol3
% 2.16/2.51 , X ), ! apart_point_and_line( X, skol2 ) }.
% 2.16/2.51 parent1[4]: (67) {G1,W15,D2,L5,V2,M3} R(10,15) { ! distinct_points( skol3,
% 2.16/2.51 X ), ! distinct_lines( skol1, Y ), apart_point_and_line( X, skol1 ),
% 2.16/2.51 apart_point_and_line( X, Y ), apart_point_and_line( skol3, Y ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := skol3
% 2.16/2.51 end
% 2.16/2.51 substitution1:
% 2.16/2.51 X := X
% 2.16/2.51 Y := skol2
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 resolution: (1584) {G1,W12,D2,L4,V1,M4} { ! distinct_points( skol3, X ), !
% 2.16/2.51 distinct_lines( skol1, skol2 ), apart_point_and_line( X, skol1 ),
% 2.16/2.51 apart_point_and_line( X, skol2 ) }.
% 2.16/2.51 parent0[0]: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 2.16/2.51 parent1[0]: (1583) {G2,W15,D2,L5,V1,M5} { distinct_points( skol3, skol3 )
% 2.16/2.51 , ! distinct_points( skol3, X ), ! distinct_lines( skol1, skol2 ),
% 2.16/2.51 apart_point_and_line( X, skol1 ), apart_point_and_line( X, skol2 ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := skol3
% 2.16/2.51 end
% 2.16/2.51 substitution1:
% 2.16/2.51 X := X
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 subsumption: (624) {G5,W12,D2,L4,V1,M1} R(67,190);r(0) { ! distinct_points
% 2.16/2.51 ( skol3, X ), ! distinct_lines( skol1, skol2 ), apart_point_and_line( X,
% 2.16/2.51 skol1 ), apart_point_and_line( X, skol2 ) }.
% 2.16/2.51 parent0: (1584) {G1,W12,D2,L4,V1,M4} { ! distinct_points( skol3, X ), !
% 2.16/2.51 distinct_lines( skol1, skol2 ), apart_point_and_line( X, skol1 ),
% 2.16/2.51 apart_point_and_line( X, skol2 ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := X
% 2.16/2.51 end
% 2.16/2.51 permutation0:
% 2.16/2.51 0 ==> 0
% 2.16/2.51 1 ==> 1
% 2.16/2.51 2 ==> 2
% 2.16/2.51 3 ==> 3
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 resolution: (1586) {G1,W16,D3,L4,V1,M4} { ! convergent_lines( X, skol2 ),
% 2.16/2.51 ! distinct_points( skol3, intersection_point( X, skol2 ) ), !
% 2.16/2.51 distinct_lines( skol1, skol2 ), apart_point_and_line( intersection_point
% 2.16/2.51 ( X, skol2 ), skol1 ) }.
% 2.16/2.51 parent0[1]: (9) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 2.16/2.51 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 2.16/2.51 parent1[3]: (624) {G5,W12,D2,L4,V1,M1} R(67,190);r(0) { ! distinct_points(
% 2.16/2.51 skol3, X ), ! distinct_lines( skol1, skol2 ), apart_point_and_line( X,
% 2.16/2.51 skol1 ), apart_point_and_line( X, skol2 ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := X
% 2.16/2.51 Y := skol2
% 2.16/2.51 end
% 2.16/2.51 substitution1:
% 2.16/2.51 X := intersection_point( X, skol2 )
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 subsumption: (790) {G6,W16,D3,L4,V1,M1} R(624,9) { ! distinct_points( skol3
% 2.16/2.51 , intersection_point( X, skol2 ) ), ! distinct_lines( skol1, skol2 ), !
% 2.16/2.51 convergent_lines( X, skol2 ), apart_point_and_line( intersection_point( X
% 2.16/2.51 , skol2 ), skol1 ) }.
% 2.16/2.51 parent0: (1586) {G1,W16,D3,L4,V1,M4} { ! convergent_lines( X, skol2 ), !
% 2.16/2.51 distinct_points( skol3, intersection_point( X, skol2 ) ), !
% 2.16/2.51 distinct_lines( skol1, skol2 ), apart_point_and_line( intersection_point
% 2.16/2.51 ( X, skol2 ), skol1 ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := X
% 2.16/2.51 end
% 2.16/2.51 permutation0:
% 2.16/2.51 0 ==> 2
% 2.16/2.51 1 ==> 0
% 2.16/2.51 2 ==> 1
% 2.16/2.51 3 ==> 3
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 resolution: (1587) {G1,W14,D3,L4,V0,M4} { ! convergent_lines( skol1, skol2
% 2.16/2.51 ), ! distinct_points( skol3, intersection_point( skol1, skol2 ) ), !
% 2.16/2.51 distinct_lines( skol1, skol2 ), ! convergent_lines( skol1, skol2 ) }.
% 2.16/2.51 parent0[1]: (8) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 2.16/2.51 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 2.16/2.51 parent1[3]: (790) {G6,W16,D3,L4,V1,M1} R(624,9) { ! distinct_points( skol3
% 2.16/2.51 , intersection_point( X, skol2 ) ), ! distinct_lines( skol1, skol2 ), !
% 2.16/2.51 convergent_lines( X, skol2 ), apart_point_and_line( intersection_point( X
% 2.16/2.51 , skol2 ), skol1 ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := skol1
% 2.16/2.51 Y := skol2
% 2.16/2.51 end
% 2.16/2.51 substitution1:
% 2.16/2.51 X := skol1
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 resolution: (1589) {G1,W9,D2,L3,V0,M3} { ! convergent_lines( skol1, skol2
% 2.16/2.51 ), ! distinct_lines( skol1, skol2 ), ! convergent_lines( skol1, skol2 )
% 2.16/2.51 }.
% 2.16/2.51 parent0[1]: (1587) {G1,W14,D3,L4,V0,M4} { ! convergent_lines( skol1, skol2
% 2.16/2.51 ), ! distinct_points( skol3, intersection_point( skol1, skol2 ) ), !
% 2.16/2.51 distinct_lines( skol1, skol2 ), ! convergent_lines( skol1, skol2 ) }.
% 2.16/2.51 parent1[0]: (17) {G0,W5,D3,L1,V0,M1} I { distinct_points( skol3,
% 2.16/2.51 intersection_point( skol1, skol2 ) ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 end
% 2.16/2.51 substitution1:
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 factor: (1590) {G1,W6,D2,L2,V0,M2} { ! convergent_lines( skol1, skol2 ), !
% 2.16/2.51 distinct_lines( skol1, skol2 ) }.
% 2.16/2.51 parent0[0, 2]: (1589) {G1,W9,D2,L3,V0,M3} { ! convergent_lines( skol1,
% 2.16/2.51 skol2 ), ! distinct_lines( skol1, skol2 ), ! convergent_lines( skol1,
% 2.16/2.51 skol2 ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 subsumption: (1292) {G7,W6,D2,L2,V0,M1} R(790,8);f;r(17) { !
% 2.16/2.51 convergent_lines( skol1, skol2 ), ! distinct_lines( skol1, skol2 ) }.
% 2.16/2.51 parent0: (1590) {G1,W6,D2,L2,V0,M2} { ! convergent_lines( skol1, skol2 ),
% 2.16/2.51 ! distinct_lines( skol1, skol2 ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 end
% 2.16/2.51 permutation0:
% 2.16/2.51 0 ==> 0
% 2.16/2.51 1 ==> 1
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 resolution: (1591) {G1,W3,D2,L1,V0,M1} { ! distinct_lines( skol1, skol2 )
% 2.16/2.51 }.
% 2.16/2.51 parent0[0]: (1292) {G7,W6,D2,L2,V0,M1} R(790,8);f;r(17) { !
% 2.16/2.51 convergent_lines( skol1, skol2 ), ! distinct_lines( skol1, skol2 ) }.
% 2.16/2.51 parent1[0]: (14) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 )
% 2.16/2.51 }.
% 2.16/2.51 substitution0:
% 2.16/2.51 end
% 2.16/2.51 substitution1:
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 subsumption: (1293) {G8,W3,D2,L1,V0,M1} S(1292);r(14) { ! distinct_lines(
% 2.16/2.51 skol1, skol2 ) }.
% 2.16/2.51 parent0: (1591) {G1,W3,D2,L1,V0,M1} { ! distinct_lines( skol1, skol2 ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 end
% 2.16/2.51 permutation0:
% 2.16/2.51 0 ==> 0
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 resolution: (1592) {G3,W6,D2,L2,V1,M2} { ! convergent_lines( X, skol2 ),
% 2.16/2.51 convergent_lines( X, skol1 ) }.
% 2.16/2.51 parent0[0]: (1293) {G8,W3,D2,L1,V0,M1} S(1292);r(14) { ! distinct_lines(
% 2.16/2.51 skol1, skol2 ) }.
% 2.16/2.51 parent1[2]: (127) {G2,W9,D2,L3,V3,M1} R(13,27) { ! convergent_lines( X, Y )
% 2.16/2.51 , convergent_lines( X, Z ), distinct_lines( Z, Y ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 end
% 2.16/2.51 substitution1:
% 2.16/2.51 X := X
% 2.16/2.51 Y := skol2
% 2.16/2.51 Z := skol1
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 resolution: (1593) {G4,W6,D2,L2,V1,M2} { convergent_lines( X, skol1 ),
% 2.16/2.51 convergent_lines( X, skol1 ) }.
% 2.16/2.51 parent0[0]: (1592) {G3,W6,D2,L2,V1,M2} { ! convergent_lines( X, skol2 ),
% 2.16/2.51 convergent_lines( X, skol1 ) }.
% 2.16/2.51 parent1[1]: (39) {G3,W6,D2,L2,V1,M1} R(37,33) { convergent_lines( X, skol1
% 2.16/2.51 ), convergent_lines( X, skol2 ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := X
% 2.16/2.51 end
% 2.16/2.51 substitution1:
% 2.16/2.51 X := X
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 factor: (1594) {G4,W3,D2,L1,V1,M1} { convergent_lines( X, skol1 ) }.
% 2.16/2.51 parent0[0, 1]: (1593) {G4,W6,D2,L2,V1,M2} { convergent_lines( X, skol1 ),
% 2.16/2.51 convergent_lines( X, skol1 ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := X
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 subsumption: (1424) {G9,W3,D2,L1,V1,M1} R(1293,127);r(39) {
% 2.16/2.51 convergent_lines( X, skol1 ) }.
% 2.16/2.51 parent0: (1594) {G4,W3,D2,L1,V1,M1} { convergent_lines( X, skol1 ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := X
% 2.16/2.51 end
% 2.16/2.51 permutation0:
% 2.16/2.51 0 ==> 0
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 resolution: (1595) {G1,W0,D0,L0,V0,M0} { }.
% 2.16/2.51 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 2.16/2.51 parent1[0]: (1424) {G9,W3,D2,L1,V1,M1} R(1293,127);r(39) { convergent_lines
% 2.16/2.51 ( X, skol1 ) }.
% 2.16/2.51 substitution0:
% 2.16/2.51 X := skol1
% 2.16/2.51 end
% 2.16/2.51 substitution1:
% 2.16/2.51 X := skol1
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 subsumption: (1443) {G10,W0,D0,L0,V0,M0} R(1424,2) { }.
% 2.16/2.51 parent0: (1595) {G1,W0,D0,L0,V0,M0} { }.
% 2.16/2.51 substitution0:
% 2.16/2.51 end
% 2.16/2.51 permutation0:
% 2.16/2.51 end
% 2.16/2.51
% 2.16/2.51 Proof check complete!
% 2.16/2.51
% 2.16/2.51 Memory use:
% 2.16/2.51
% 2.16/2.51 space for terms: 22582
% 2.16/2.51 space for clauses: 52008
% 2.16/2.51
% 2.16/2.51
% 2.16/2.51 clauses generated: 174364
% 2.16/2.51 clauses kept: 1444
% 2.16/2.51 clauses selected: 990
% 2.16/2.51 clauses deleted: 9
% 2.16/2.51 clauses inuse deleted: 0
% 2.16/2.51
% 2.16/2.51 subsentry: 185274
% 2.16/2.51 literals s-matched: 117776
% 2.16/2.51 literals matched: 117741
% 2.16/2.51 full subsumption: 69246
% 2.16/2.51
% 2.16/2.51 checksum: -10310973
% 2.16/2.51
% 2.16/2.51
% 2.16/2.51 Bliksem ended
%------------------------------------------------------------------------------