TSTP Solution File: GEO174+2 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO174+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n018.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 1.10s 1.48s
% Output : Refutation 1.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO174+2 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n018.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 : Sat Jun 18 13:30:48 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.10/1.48 *** allocated 10000 integers for termspace/termends
% 1.10/1.48 *** allocated 10000 integers for clauses
% 1.10/1.48 *** allocated 10000 integers for justifications
% 1.10/1.48 Bliksem 1.12
% 1.10/1.48
% 1.10/1.48
% 1.10/1.48 Automatic Strategy Selection
% 1.10/1.48
% 1.10/1.48
% 1.10/1.48 Clauses:
% 1.10/1.48
% 1.10/1.48 { ! distinct_points( X, X ) }.
% 1.10/1.48 { ! distinct_lines( X, X ) }.
% 1.10/1.48 { ! convergent_lines( X, X ) }.
% 1.10/1.48 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 1.10/1.48 ) }.
% 1.10/1.48 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 1.10/1.48 }.
% 1.10/1.48 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 1.10/1.48 , Z ) }.
% 1.10/1.48 { ! distinct_points( X, Y ), ! apart_point_and_line( Z, line_connecting( X
% 1.10/1.48 , Y ) ), distinct_points( Z, X ) }.
% 1.10/1.48 { ! distinct_points( X, Y ), ! apart_point_and_line( Z, line_connecting( X
% 1.10/1.48 , Y ) ), distinct_points( Z, Y ) }.
% 1.10/1.48 { ! convergent_lines( X, Y ), ! apart_point_and_line( Z, X ),
% 1.10/1.48 distinct_points( Z, intersection_point( X, Y ) ) }.
% 1.10/1.48 { ! convergent_lines( X, Y ), ! apart_point_and_line( Z, Y ),
% 1.10/1.48 distinct_points( Z, intersection_point( X, Y ) ) }.
% 1.10/1.48 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 1.10/1.48 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 1.10/1.48 apart_point_and_line( Y, T ) }.
% 1.10/1.48 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 1.10/1.48 apart_point_and_line( Z, Y ) }.
% 1.10/1.48 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 1.10/1.48 apart_point_and_line( X, Z ) }.
% 1.10/1.48 { ! convergent_lines( X, Y ), distinct_lines( X, Y ) }.
% 1.10/1.48 { distinct_points( skol1, skol2 ) }.
% 1.10/1.48 { convergent_lines( skol3, skol4 ) }.
% 1.10/1.48 { apart_point_and_line( skol1, skol3 ), apart_point_and_line( skol2, skol3
% 1.10/1.48 ) }.
% 1.10/1.48 { ! distinct_lines( skol3, line_connecting( skol1, skol2 ) ) }.
% 1.10/1.48
% 1.10/1.48 percentage equality = 0.000000, percentage horn = 0.611111
% 1.10/1.48 This a non-horn, non-equality problem
% 1.10/1.48
% 1.10/1.48
% 1.10/1.48 Options Used:
% 1.10/1.48
% 1.10/1.48 useres = 1
% 1.10/1.48 useparamod = 0
% 1.10/1.48 useeqrefl = 0
% 1.10/1.48 useeqfact = 0
% 1.10/1.48 usefactor = 1
% 1.10/1.48 usesimpsplitting = 0
% 1.10/1.48 usesimpdemod = 0
% 1.10/1.48 usesimpres = 3
% 1.10/1.48
% 1.10/1.48 resimpinuse = 1000
% 1.10/1.48 resimpclauses = 20000
% 1.10/1.48 substype = standard
% 1.10/1.48 backwardsubs = 1
% 1.10/1.48 selectoldest = 5
% 1.10/1.48
% 1.10/1.48 litorderings [0] = split
% 1.10/1.48 litorderings [1] = liftord
% 1.10/1.48
% 1.10/1.48 termordering = none
% 1.10/1.48
% 1.10/1.48 litapriori = 1
% 1.10/1.48 termapriori = 0
% 1.10/1.48 litaposteriori = 0
% 1.10/1.48 termaposteriori = 0
% 1.10/1.48 demodaposteriori = 0
% 1.10/1.48 ordereqreflfact = 0
% 1.10/1.48
% 1.10/1.48 litselect = none
% 1.10/1.48
% 1.10/1.48 maxweight = 15
% 1.10/1.48 maxdepth = 30000
% 1.10/1.48 maxlength = 115
% 1.10/1.48 maxnrvars = 195
% 1.10/1.48 excuselevel = 1
% 1.10/1.48 increasemaxweight = 1
% 1.10/1.48
% 1.10/1.48 maxselected = 10000000
% 1.10/1.48 maxnrclauses = 10000000
% 1.10/1.48
% 1.10/1.48 showgenerated = 0
% 1.10/1.48 showkept = 0
% 1.10/1.48 showselected = 0
% 1.10/1.48 showdeleted = 0
% 1.10/1.48 showresimp = 1
% 1.10/1.48 showstatus = 2000
% 1.10/1.48
% 1.10/1.48 prologoutput = 0
% 1.10/1.48 nrgoals = 5000000
% 1.10/1.48 totalproof = 1
% 1.10/1.48
% 1.10/1.48 Symbols occurring in the translation:
% 1.10/1.48
% 1.10/1.48 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.10/1.48 . [1, 2] (w:1, o:20, a:1, s:1, b:0),
% 1.10/1.48 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 1.10/1.48 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.10/1.48 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.10/1.48 distinct_points [36, 2] (w:1, o:45, a:1, s:1, b:0),
% 1.10/1.48 distinct_lines [37, 2] (w:1, o:46, a:1, s:1, b:0),
% 1.10/1.48 convergent_lines [38, 2] (w:1, o:44, a:1, s:1, b:0),
% 1.10/1.48 line_connecting [41, 2] (w:1, o:47, a:1, s:1, b:0),
% 1.10/1.48 apart_point_and_line [42, 2] (w:1, o:48, a:1, s:1, b:0),
% 1.10/1.48 intersection_point [43, 2] (w:1, o:49, a:1, s:1, b:0),
% 1.10/1.48 skol1 [46, 0] (w:1, o:11, a:1, s:1, b:0),
% 1.10/1.48 skol2 [47, 0] (w:1, o:12, a:1, s:1, b:0),
% 1.10/1.48 skol3 [48, 0] (w:1, o:13, a:1, s:1, b:0),
% 1.10/1.48 skol4 [49, 0] (w:1, o:14, a:1, s:1, b:0).
% 1.10/1.48
% 1.10/1.48
% 1.10/1.48 Starting Search:
% 1.10/1.48
% 1.10/1.48 *** allocated 15000 integers for clauses
% 1.10/1.48 *** allocated 22500 integers for clauses
% 1.10/1.48 *** allocated 33750 integers for clauses
% 1.10/1.48 *** allocated 15000 integers for termspace/termends
% 1.10/1.48 *** allocated 50625 integers for clauses
% 1.10/1.48 Resimplifying inuse:
% 1.10/1.48 Done
% 1.10/1.48
% 1.10/1.48 *** allocated 22500 integers for termspace/termends
% 1.10/1.48
% 1.10/1.48 Bliksems!, er is een bewijs:
% 1.10/1.48 % SZS status Theorem
% 1.10/1.48 % SZS output start Refutation
% 1.10/1.48
% 1.10/1.48 (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 1.10/1.48 (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 1.10/1.48 (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 1.10/1.48 , ! distinct_lines( X, Y ) }.
% 1.10/1.48 (6) {G0,W11,D3,L3,V3,M1} I { ! distinct_points( X, Y ), distinct_points( Z
% 1.10/1.48 , X ), ! apart_point_and_line( Z, line_connecting( X, Y ) ) }.
% 1.10/1.48 (7) {G0,W11,D3,L3,V3,M1} I { ! distinct_points( X, Y ), distinct_points( Z
% 1.10/1.48 , Y ), ! apart_point_and_line( Z, line_connecting( X, Y ) ) }.
% 1.10/1.48 (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), apart_point_and_line
% 1.10/1.48 ( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 1.10/1.48 (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), apart_point_and_line(
% 1.10/1.48 X, Z ), ! apart_point_and_line( X, Y ) }.
% 1.10/1.48 (14) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol1, skol2 ) }.
% 1.10/1.48 (16) {G0,W6,D2,L2,V0,M1} I { apart_point_and_line( skol1, skol3 ),
% 1.10/1.48 apart_point_and_line( skol2, skol3 ) }.
% 1.10/1.48 (17) {G0,W5,D3,L1,V0,M1} I { ! distinct_lines( skol3, line_connecting(
% 1.10/1.48 skol1, skol2 ) ) }.
% 1.10/1.48 (31) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 1.10/1.48 ( X, Y ) }.
% 1.10/1.48 (35) {G2,W5,D3,L1,V0,M1} R(31,17) { ! distinct_lines( line_connecting(
% 1.10/1.48 skol1, skol2 ), skol3 ) }.
% 1.10/1.48 (114) {G1,W14,D3,L4,V4,M1} R(11,7) { distinct_points( X, Y ), !
% 1.10/1.48 distinct_points( Z, T ), distinct_points( Y, T ), ! apart_point_and_line
% 1.10/1.48 ( X, line_connecting( Z, T ) ) }.
% 1.10/1.48 (115) {G1,W14,D3,L4,V4,M1} R(11,6) { distinct_points( X, Y ), !
% 1.10/1.48 distinct_points( Z, T ), distinct_points( Y, Z ), ! apart_point_and_line
% 1.10/1.48 ( X, line_connecting( Z, T ) ) }.
% 1.10/1.48 (116) {G2,W8,D3,L2,V2,M1} F(115);r(0) { ! distinct_points( X, Y ), !
% 1.10/1.48 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.10/1.48 (117) {G2,W8,D3,L2,V2,M1} F(114);r(0) { ! distinct_points( Y, X ), !
% 1.10/1.48 apart_point_and_line( X, line_connecting( Y, X ) ) }.
% 1.10/1.48 (120) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ),
% 1.10/1.48 distinct_lines( Y, T ), apart_point_and_line( Z, T ), !
% 1.10/1.48 apart_point_and_line( Z, X ) }.
% 1.10/1.48 (792) {G2,W15,D2,L5,V5,M2} R(120,12) { distinct_lines( X, Y ),
% 1.10/1.48 distinct_lines( Y, Z ), distinct_lines( Z, U ), apart_point_and_line( T,
% 1.10/1.48 U ), ! apart_point_and_line( T, X ) }.
% 1.10/1.48 (794) {G3,W9,D2,L3,V3,M2} F(792);r(31) { distinct_lines( Y, X ), !
% 1.10/1.48 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ) }.
% 1.10/1.48 (829) {G4,W11,D3,L3,V3,M1} R(794,116) { distinct_lines( line_connecting( X
% 1.10/1.48 , Y ), Z ), ! distinct_points( X, Y ), ! apart_point_and_line( X, Z ) }.
% 1.10/1.48 (835) {G4,W9,D2,L3,V1,M2} R(794,16) { distinct_lines( X, skol3 ),
% 1.10/1.48 apart_point_and_line( skol1, skol3 ), apart_point_and_line( skol2, X )
% 1.10/1.48 }.
% 1.10/1.48 (992) {G5,W14,D3,L4,V2,M1} R(829,835) { ! distinct_points( skol1, X ),
% 1.10/1.48 distinct_lines( line_connecting( skol1, X ), skol3 ), distinct_lines( Y,
% 1.10/1.48 skol3 ), apart_point_and_line( skol2, Y ) }.
% 1.10/1.48 (1008) {G6,W13,D3,L3,V1,M1} F(992) { ! distinct_points( skol1, X ),
% 1.10/1.48 distinct_lines( line_connecting( skol1, X ), skol3 ),
% 1.10/1.48 apart_point_and_line( skol2, line_connecting( skol1, X ) ) }.
% 1.10/1.48 (1309) {G7,W5,D3,L1,V0,M1} R(1008,117);f;r(14) { distinct_lines(
% 1.10/1.48 line_connecting( skol1, skol2 ), skol3 ) }.
% 1.10/1.48 (1311) {G8,W0,D0,L0,V0,M0} S(1309);r(35) { }.
% 1.10/1.48
% 1.10/1.48
% 1.10/1.48 % SZS output end Refutation
% 1.10/1.48 found a proof!
% 1.10/1.48
% 1.10/1.48
% 1.10/1.48 Unprocessed initial clauses:
% 1.10/1.48
% 1.10/1.48 (1313) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 1.10/1.48 (1314) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 1.10/1.48 (1315) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 1.10/1.48 (1316) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 1.10/1.48 , Z ), distinct_points( Y, Z ) }.
% 1.10/1.48 (1317) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X,
% 1.10/1.48 Z ), distinct_lines( Y, Z ) }.
% 1.10/1.48 (1318) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines
% 1.10/1.48 ( X, Z ), convergent_lines( Y, Z ) }.
% 1.10/1.48 (1319) {G0,W11,D3,L3,V3,M3} { ! distinct_points( X, Y ), !
% 1.10/1.48 apart_point_and_line( Z, line_connecting( X, Y ) ), distinct_points( Z, X
% 1.10/1.48 ) }.
% 1.10/1.48 (1320) {G0,W11,D3,L3,V3,M3} { ! distinct_points( X, Y ), !
% 1.10/1.48 apart_point_and_line( Z, line_connecting( X, Y ) ), distinct_points( Z, Y
% 1.10/1.48 ) }.
% 1.10/1.48 (1321) {G0,W11,D3,L3,V3,M3} { ! convergent_lines( X, Y ), !
% 1.10/1.48 apart_point_and_line( Z, X ), distinct_points( Z, intersection_point( X,
% 1.10/1.48 Y ) ) }.
% 1.10/1.48 (1322) {G0,W11,D3,L3,V3,M3} { ! convergent_lines( X, Y ), !
% 1.10/1.48 apart_point_and_line( Z, Y ), distinct_points( Z, intersection_point( X,
% 1.10/1.48 Y ) ) }.
% 1.10/1.48 (1323) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines
% 1.10/1.48 ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 1.10/1.48 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 1.10/1.48 (1324) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 1.10/1.48 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 1.10/1.48 (1325) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 1.10/1.48 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 1.10/1.48 (1326) {G0,W6,D2,L2,V2,M2} { ! convergent_lines( X, Y ), distinct_lines( X
% 1.10/1.48 , Y ) }.
% 1.10/1.48 (1327) {G0,W3,D2,L1,V0,M1} { distinct_points( skol1, skol2 ) }.
% 1.10/1.48 (1328) {G0,W3,D2,L1,V0,M1} { convergent_lines( skol3, skol4 ) }.
% 1.10/1.48 (1329) {G0,W6,D2,L2,V0,M2} { apart_point_and_line( skol1, skol3 ),
% 1.10/1.48 apart_point_and_line( skol2, skol3 ) }.
% 1.10/1.48 (1330) {G0,W5,D3,L1,V0,M1} { ! distinct_lines( skol3, line_connecting(
% 1.10/1.48 skol1, skol2 ) ) }.
% 1.10/1.48
% 1.10/1.48
% 1.10/1.48 Total Proof:
% 1.10/1.48
% 1.10/1.48 subsumption: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 1.10/1.48 parent0: (1313) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := X
% 1.10/1.48 end
% 1.10/1.48 permutation0:
% 1.10/1.48 0 ==> 0
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 1.10/1.48 parent0: (1314) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := X
% 1.10/1.48 end
% 1.10/1.48 permutation0:
% 1.10/1.48 0 ==> 0
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 1.10/1.48 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 1.10/1.48 parent0: (1317) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ),
% 1.10/1.48 distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := X
% 1.10/1.48 Y := Y
% 1.10/1.48 Z := Z
% 1.10/1.48 end
% 1.10/1.48 permutation0:
% 1.10/1.48 0 ==> 2
% 1.10/1.48 1 ==> 0
% 1.10/1.48 2 ==> 1
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 subsumption: (6) {G0,W11,D3,L3,V3,M1} I { ! distinct_points( X, Y ),
% 1.10/1.48 distinct_points( Z, X ), ! apart_point_and_line( Z, line_connecting( X, Y
% 1.10/1.48 ) ) }.
% 1.10/1.48 parent0: (1319) {G0,W11,D3,L3,V3,M3} { ! distinct_points( X, Y ), !
% 1.10/1.48 apart_point_and_line( Z, line_connecting( X, Y ) ), distinct_points( Z, X
% 1.10/1.48 ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := X
% 1.10/1.48 Y := Y
% 1.10/1.48 Z := Z
% 1.10/1.48 end
% 1.10/1.48 permutation0:
% 1.10/1.48 0 ==> 0
% 1.10/1.48 1 ==> 2
% 1.10/1.48 2 ==> 1
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 subsumption: (7) {G0,W11,D3,L3,V3,M1} I { ! distinct_points( X, Y ),
% 1.10/1.48 distinct_points( Z, Y ), ! apart_point_and_line( Z, line_connecting( X, Y
% 1.10/1.48 ) ) }.
% 1.10/1.48 parent0: (1320) {G0,W11,D3,L3,V3,M3} { ! distinct_points( X, Y ), !
% 1.10/1.48 apart_point_and_line( Z, line_connecting( X, Y ) ), distinct_points( Z, Y
% 1.10/1.48 ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := X
% 1.10/1.48 Y := Y
% 1.10/1.48 Z := Z
% 1.10/1.48 end
% 1.10/1.48 permutation0:
% 1.10/1.48 0 ==> 0
% 1.10/1.48 1 ==> 2
% 1.10/1.48 2 ==> 1
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 subsumption: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ),
% 1.10/1.48 apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 1.10/1.48 parent0: (1324) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 1.10/1.48 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := X
% 1.10/1.48 Y := Y
% 1.10/1.48 Z := Z
% 1.10/1.48 end
% 1.10/1.48 permutation0:
% 1.10/1.48 0 ==> 2
% 1.10/1.48 1 ==> 0
% 1.10/1.48 2 ==> 1
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 subsumption: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 1.10/1.48 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 1.10/1.48 parent0: (1325) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 1.10/1.48 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := X
% 1.10/1.48 Y := Y
% 1.10/1.48 Z := Z
% 1.10/1.48 end
% 1.10/1.48 permutation0:
% 1.10/1.48 0 ==> 2
% 1.10/1.48 1 ==> 0
% 1.10/1.48 2 ==> 1
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 subsumption: (14) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol1, skol2 )
% 1.10/1.48 }.
% 1.10/1.48 parent0: (1327) {G0,W3,D2,L1,V0,M1} { distinct_points( skol1, skol2 ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 end
% 1.10/1.48 permutation0:
% 1.10/1.48 0 ==> 0
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 subsumption: (16) {G0,W6,D2,L2,V0,M1} I { apart_point_and_line( skol1,
% 1.10/1.48 skol3 ), apart_point_and_line( skol2, skol3 ) }.
% 1.10/1.48 parent0: (1329) {G0,W6,D2,L2,V0,M2} { apart_point_and_line( skol1, skol3 )
% 1.10/1.48 , apart_point_and_line( skol2, skol3 ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 end
% 1.10/1.48 permutation0:
% 1.10/1.48 0 ==> 0
% 1.10/1.48 1 ==> 1
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 subsumption: (17) {G0,W5,D3,L1,V0,M1} I { ! distinct_lines( skol3,
% 1.10/1.48 line_connecting( skol1, skol2 ) ) }.
% 1.10/1.48 parent0: (1330) {G0,W5,D3,L1,V0,M1} { ! distinct_lines( skol3,
% 1.10/1.48 line_connecting( skol1, skol2 ) ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 end
% 1.10/1.48 permutation0:
% 1.10/1.48 0 ==> 0
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 resolution: (1384) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 1.10/1.48 distinct_lines( X, Y ) }.
% 1.10/1.48 parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 1.10/1.48 parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 1.10/1.48 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := X
% 1.10/1.48 end
% 1.10/1.48 substitution1:
% 1.10/1.48 X := X
% 1.10/1.48 Y := Y
% 1.10/1.48 Z := X
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 subsumption: (31) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 1.10/1.48 distinct_lines( X, Y ) }.
% 1.10/1.48 parent0: (1384) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 1.10/1.48 distinct_lines( X, Y ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := Y
% 1.10/1.48 Y := X
% 1.10/1.48 end
% 1.10/1.48 permutation0:
% 1.10/1.48 0 ==> 1
% 1.10/1.48 1 ==> 0
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 resolution: (1386) {G1,W5,D3,L1,V0,M1} { ! distinct_lines( line_connecting
% 1.10/1.48 ( skol1, skol2 ), skol3 ) }.
% 1.10/1.48 parent0[0]: (17) {G0,W5,D3,L1,V0,M1} I { ! distinct_lines( skol3,
% 1.10/1.48 line_connecting( skol1, skol2 ) ) }.
% 1.10/1.48 parent1[1]: (31) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 1.10/1.48 distinct_lines( X, Y ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 end
% 1.10/1.48 substitution1:
% 1.10/1.48 X := skol3
% 1.10/1.48 Y := line_connecting( skol1, skol2 )
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 subsumption: (35) {G2,W5,D3,L1,V0,M1} R(31,17) { ! distinct_lines(
% 1.10/1.48 line_connecting( skol1, skol2 ), skol3 ) }.
% 1.10/1.48 parent0: (1386) {G1,W5,D3,L1,V0,M1} { ! distinct_lines( line_connecting(
% 1.10/1.48 skol1, skol2 ), skol3 ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 end
% 1.10/1.48 permutation0:
% 1.10/1.48 0 ==> 0
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 resolution: (1388) {G1,W14,D3,L4,V4,M4} { ! distinct_points( X, Y ),
% 1.10/1.48 distinct_points( Z, Y ), distinct_points( T, Z ), ! apart_point_and_line
% 1.10/1.48 ( T, line_connecting( X, Y ) ) }.
% 1.10/1.48 parent0[2]: (7) {G0,W11,D3,L3,V3,M1} I { ! distinct_points( X, Y ),
% 1.10/1.48 distinct_points( Z, Y ), ! apart_point_and_line( Z, line_connecting( X, Y
% 1.10/1.48 ) ) }.
% 1.10/1.48 parent1[1]: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ),
% 1.10/1.48 apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := X
% 1.10/1.48 Y := Y
% 1.10/1.48 Z := Z
% 1.10/1.48 end
% 1.10/1.48 substitution1:
% 1.10/1.48 X := T
% 1.10/1.48 Y := line_connecting( X, Y )
% 1.10/1.48 Z := Z
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 subsumption: (114) {G1,W14,D3,L4,V4,M1} R(11,7) { distinct_points( X, Y ),
% 1.10/1.48 ! distinct_points( Z, T ), distinct_points( Y, T ), !
% 1.10/1.48 apart_point_and_line( X, line_connecting( Z, T ) ) }.
% 1.10/1.48 parent0: (1388) {G1,W14,D3,L4,V4,M4} { ! distinct_points( X, Y ),
% 1.10/1.48 distinct_points( Z, Y ), distinct_points( T, Z ), ! apart_point_and_line
% 1.10/1.48 ( T, line_connecting( X, Y ) ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := Z
% 1.10/1.48 Y := T
% 1.10/1.48 Z := Y
% 1.10/1.48 T := X
% 1.10/1.48 end
% 1.10/1.48 permutation0:
% 1.10/1.48 0 ==> 1
% 1.10/1.48 1 ==> 2
% 1.10/1.48 2 ==> 0
% 1.10/1.48 3 ==> 3
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 resolution: (1392) {G1,W14,D3,L4,V4,M4} { ! distinct_points( X, Y ),
% 1.10/1.48 distinct_points( Z, X ), distinct_points( T, Z ), ! apart_point_and_line
% 1.10/1.48 ( T, line_connecting( X, Y ) ) }.
% 1.10/1.48 parent0[2]: (6) {G0,W11,D3,L3,V3,M1} I { ! distinct_points( X, Y ),
% 1.10/1.48 distinct_points( Z, X ), ! apart_point_and_line( Z, line_connecting( X, Y
% 1.10/1.48 ) ) }.
% 1.10/1.48 parent1[1]: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ),
% 1.10/1.48 apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := X
% 1.10/1.48 Y := Y
% 1.10/1.48 Z := Z
% 1.10/1.48 end
% 1.10/1.48 substitution1:
% 1.10/1.48 X := T
% 1.10/1.48 Y := line_connecting( X, Y )
% 1.10/1.48 Z := Z
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 subsumption: (115) {G1,W14,D3,L4,V4,M1} R(11,6) { distinct_points( X, Y ),
% 1.10/1.48 ! distinct_points( Z, T ), distinct_points( Y, Z ), !
% 1.10/1.48 apart_point_and_line( X, line_connecting( Z, T ) ) }.
% 1.10/1.48 parent0: (1392) {G1,W14,D3,L4,V4,M4} { ! distinct_points( X, Y ),
% 1.10/1.48 distinct_points( Z, X ), distinct_points( T, Z ), ! apart_point_and_line
% 1.10/1.48 ( T, line_connecting( X, Y ) ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := Z
% 1.10/1.48 Y := T
% 1.10/1.48 Z := Y
% 1.10/1.48 T := X
% 1.10/1.48 end
% 1.10/1.48 permutation0:
% 1.10/1.48 0 ==> 1
% 1.10/1.48 1 ==> 2
% 1.10/1.48 2 ==> 0
% 1.10/1.48 3 ==> 3
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 factor: (1395) {G1,W11,D3,L3,V2,M3} { distinct_points( X, X ), !
% 1.10/1.48 distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X, Y
% 1.10/1.48 ) ) }.
% 1.10/1.48 parent0[0, 2]: (115) {G1,W14,D3,L4,V4,M1} R(11,6) { distinct_points( X, Y )
% 1.10/1.48 , ! distinct_points( Z, T ), distinct_points( Y, Z ), !
% 1.10/1.48 apart_point_and_line( X, line_connecting( Z, T ) ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := X
% 1.10/1.48 Y := X
% 1.10/1.48 Z := X
% 1.10/1.48 T := Y
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 resolution: (1396) {G1,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 1.10/1.48 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.10/1.48 parent0[0]: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 1.10/1.48 parent1[0]: (1395) {G1,W11,D3,L3,V2,M3} { distinct_points( X, X ), !
% 1.10/1.48 distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X, Y
% 1.10/1.48 ) ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := X
% 1.10/1.48 end
% 1.10/1.48 substitution1:
% 1.10/1.48 X := X
% 1.10/1.48 Y := Y
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 subsumption: (116) {G2,W8,D3,L2,V2,M1} F(115);r(0) { ! distinct_points( X,
% 1.10/1.48 Y ), ! apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.10/1.48 parent0: (1396) {G1,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 1.10/1.48 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := X
% 1.10/1.48 Y := Y
% 1.10/1.48 end
% 1.10/1.48 permutation0:
% 1.10/1.48 0 ==> 0
% 1.10/1.48 1 ==> 1
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 factor: (1397) {G1,W11,D3,L3,V2,M3} { distinct_points( X, X ), !
% 1.10/1.48 distinct_points( Y, X ), ! apart_point_and_line( X, line_connecting( Y, X
% 1.10/1.48 ) ) }.
% 1.10/1.48 parent0[0, 2]: (114) {G1,W14,D3,L4,V4,M1} R(11,7) { distinct_points( X, Y )
% 1.10/1.48 , ! distinct_points( Z, T ), distinct_points( Y, T ), !
% 1.10/1.48 apart_point_and_line( X, line_connecting( Z, T ) ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := X
% 1.10/1.48 Y := X
% 1.10/1.48 Z := Y
% 1.10/1.48 T := X
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 resolution: (1398) {G1,W8,D3,L2,V2,M2} { ! distinct_points( Y, X ), !
% 1.10/1.48 apart_point_and_line( X, line_connecting( Y, X ) ) }.
% 1.10/1.48 parent0[0]: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 1.10/1.48 parent1[0]: (1397) {G1,W11,D3,L3,V2,M3} { distinct_points( X, X ), !
% 1.10/1.48 distinct_points( Y, X ), ! apart_point_and_line( X, line_connecting( Y, X
% 1.10/1.48 ) ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := X
% 1.10/1.48 end
% 1.10/1.48 substitution1:
% 1.10/1.48 X := X
% 1.10/1.48 Y := Y
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 subsumption: (117) {G2,W8,D3,L2,V2,M1} F(114);r(0) { ! distinct_points( Y,
% 1.10/1.48 X ), ! apart_point_and_line( X, line_connecting( Y, X ) ) }.
% 1.10/1.48 parent0: (1398) {G1,W8,D3,L2,V2,M2} { ! distinct_points( Y, X ), !
% 1.10/1.48 apart_point_and_line( X, line_connecting( Y, X ) ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := X
% 1.10/1.48 Y := Y
% 1.10/1.48 end
% 1.10/1.48 permutation0:
% 1.10/1.48 0 ==> 0
% 1.10/1.48 1 ==> 1
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 resolution: (1399) {G1,W12,D2,L4,V4,M4} { distinct_lines( X, Y ),
% 1.10/1.48 apart_point_and_line( Z, Y ), distinct_lines( T, X ), !
% 1.10/1.48 apart_point_and_line( Z, T ) }.
% 1.10/1.48 parent0[2]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 1.10/1.48 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 1.10/1.48 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 1.10/1.48 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := Z
% 1.10/1.48 Y := X
% 1.10/1.48 Z := Y
% 1.10/1.48 end
% 1.10/1.48 substitution1:
% 1.10/1.48 X := Z
% 1.10/1.48 Y := T
% 1.10/1.48 Z := X
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 subsumption: (120) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ),
% 1.10/1.48 distinct_lines( Y, T ), apart_point_and_line( Z, T ), !
% 1.10/1.48 apart_point_and_line( Z, X ) }.
% 1.10/1.48 parent0: (1399) {G1,W12,D2,L4,V4,M4} { distinct_lines( X, Y ),
% 1.10/1.48 apart_point_and_line( Z, Y ), distinct_lines( T, X ), !
% 1.10/1.48 apart_point_and_line( Z, T ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := Y
% 1.10/1.48 Y := T
% 1.10/1.48 Z := Z
% 1.10/1.48 T := X
% 1.10/1.48 end
% 1.10/1.48 permutation0:
% 1.10/1.48 0 ==> 1
% 1.10/1.48 1 ==> 2
% 1.10/1.48 2 ==> 0
% 1.10/1.48 3 ==> 3
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 resolution: (1401) {G1,W15,D2,L5,V5,M5} { distinct_lines( X, Y ),
% 1.10/1.48 distinct_lines( Y, Z ), apart_point_and_line( T, Z ), distinct_lines( U,
% 1.10/1.48 X ), ! apart_point_and_line( T, U ) }.
% 1.10/1.48 parent0[3]: (120) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ),
% 1.10/1.48 distinct_lines( Y, T ), apart_point_and_line( Z, T ), !
% 1.10/1.48 apart_point_and_line( Z, X ) }.
% 1.10/1.48 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 1.10/1.48 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := X
% 1.10/1.48 Y := Y
% 1.10/1.48 Z := T
% 1.10/1.48 T := Z
% 1.10/1.48 end
% 1.10/1.48 substitution1:
% 1.10/1.48 X := T
% 1.10/1.48 Y := U
% 1.10/1.48 Z := X
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 subsumption: (792) {G2,W15,D2,L5,V5,M2} R(120,12) { distinct_lines( X, Y )
% 1.10/1.48 , distinct_lines( Y, Z ), distinct_lines( Z, U ), apart_point_and_line( T
% 1.10/1.48 , U ), ! apart_point_and_line( T, X ) }.
% 1.10/1.48 parent0: (1401) {G1,W15,D2,L5,V5,M5} { distinct_lines( X, Y ),
% 1.10/1.48 distinct_lines( Y, Z ), apart_point_and_line( T, Z ), distinct_lines( U,
% 1.10/1.48 X ), ! apart_point_and_line( T, U ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := Y
% 1.10/1.48 Y := Z
% 1.10/1.48 Z := U
% 1.10/1.48 T := T
% 1.10/1.48 U := X
% 1.10/1.48 end
% 1.10/1.48 permutation0:
% 1.10/1.48 0 ==> 1
% 1.10/1.48 1 ==> 2
% 1.10/1.48 2 ==> 3
% 1.10/1.48 3 ==> 0
% 1.10/1.48 4 ==> 4
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 factor: (1407) {G2,W12,D2,L4,V3,M4} { distinct_lines( X, Y ),
% 1.10/1.48 distinct_lines( Y, X ), apart_point_and_line( Z, Y ), !
% 1.10/1.48 apart_point_and_line( Z, X ) }.
% 1.10/1.48 parent0[0, 2]: (792) {G2,W15,D2,L5,V5,M2} R(120,12) { distinct_lines( X, Y
% 1.10/1.48 ), distinct_lines( Y, Z ), distinct_lines( Z, U ), apart_point_and_line
% 1.10/1.48 ( T, U ), ! apart_point_and_line( T, X ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := X
% 1.10/1.48 Y := Y
% 1.10/1.48 Z := X
% 1.10/1.48 T := Z
% 1.10/1.48 U := Y
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 resolution: (1413) {G2,W12,D2,L4,V3,M4} { distinct_lines( Y, X ),
% 1.10/1.48 distinct_lines( Y, X ), apart_point_and_line( Z, Y ), !
% 1.10/1.48 apart_point_and_line( Z, X ) }.
% 1.10/1.48 parent0[0]: (31) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 1.10/1.48 distinct_lines( X, Y ) }.
% 1.10/1.48 parent1[0]: (1407) {G2,W12,D2,L4,V3,M4} { distinct_lines( X, Y ),
% 1.10/1.48 distinct_lines( Y, X ), apart_point_and_line( Z, Y ), !
% 1.10/1.48 apart_point_and_line( Z, X ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := Y
% 1.10/1.48 Y := X
% 1.10/1.48 end
% 1.10/1.48 substitution1:
% 1.10/1.48 X := X
% 1.10/1.48 Y := Y
% 1.10/1.48 Z := Z
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 factor: (1415) {G2,W9,D2,L3,V3,M3} { distinct_lines( X, Y ),
% 1.10/1.48 apart_point_and_line( Z, X ), ! apart_point_and_line( Z, Y ) }.
% 1.10/1.48 parent0[0, 1]: (1413) {G2,W12,D2,L4,V3,M4} { distinct_lines( Y, X ),
% 1.10/1.48 distinct_lines( Y, X ), apart_point_and_line( Z, Y ), !
% 1.10/1.48 apart_point_and_line( Z, X ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := Y
% 1.10/1.48 Y := X
% 1.10/1.48 Z := Z
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 subsumption: (794) {G3,W9,D2,L3,V3,M2} F(792);r(31) { distinct_lines( Y, X
% 1.10/1.48 ), ! apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ) }.
% 1.10/1.48 parent0: (1415) {G2,W9,D2,L3,V3,M3} { distinct_lines( X, Y ),
% 1.10/1.48 apart_point_and_line( Z, X ), ! apart_point_and_line( Z, Y ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := Y
% 1.10/1.48 Y := X
% 1.10/1.48 Z := Z
% 1.10/1.48 end
% 1.10/1.48 permutation0:
% 1.10/1.48 0 ==> 0
% 1.10/1.48 1 ==> 2
% 1.10/1.48 2 ==> 1
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 resolution: (1417) {G3,W11,D3,L3,V3,M3} { ! distinct_points( X, Y ),
% 1.10/1.48 distinct_lines( line_connecting( X, Y ), Z ), ! apart_point_and_line( X,
% 1.10/1.48 Z ) }.
% 1.10/1.48 parent0[1]: (116) {G2,W8,D3,L2,V2,M1} F(115);r(0) { ! distinct_points( X, Y
% 1.10/1.48 ), ! apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.10/1.48 parent1[2]: (794) {G3,W9,D2,L3,V3,M2} F(792);r(31) { distinct_lines( Y, X )
% 1.10/1.48 , ! apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := X
% 1.10/1.48 Y := Y
% 1.10/1.48 end
% 1.10/1.48 substitution1:
% 1.10/1.48 X := Z
% 1.10/1.48 Y := line_connecting( X, Y )
% 1.10/1.48 Z := X
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 subsumption: (829) {G4,W11,D3,L3,V3,M1} R(794,116) { distinct_lines(
% 1.10/1.48 line_connecting( X, Y ), Z ), ! distinct_points( X, Y ), !
% 1.10/1.48 apart_point_and_line( X, Z ) }.
% 1.10/1.48 parent0: (1417) {G3,W11,D3,L3,V3,M3} { ! distinct_points( X, Y ),
% 1.10/1.48 distinct_lines( line_connecting( X, Y ), Z ), ! apart_point_and_line( X,
% 1.10/1.48 Z ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := X
% 1.10/1.48 Y := Y
% 1.10/1.48 Z := Z
% 1.10/1.48 end
% 1.10/1.48 permutation0:
% 1.10/1.48 0 ==> 1
% 1.10/1.48 1 ==> 0
% 1.10/1.48 2 ==> 2
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 resolution: (1419) {G1,W9,D2,L3,V1,M3} { distinct_lines( X, skol3 ),
% 1.10/1.48 apart_point_and_line( skol2, X ), apart_point_and_line( skol1, skol3 )
% 1.10/1.48 }.
% 1.10/1.48 parent0[1]: (794) {G3,W9,D2,L3,V3,M2} F(792);r(31) { distinct_lines( Y, X )
% 1.10/1.48 , ! apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ) }.
% 1.10/1.48 parent1[1]: (16) {G0,W6,D2,L2,V0,M1} I { apart_point_and_line( skol1, skol3
% 1.10/1.48 ), apart_point_and_line( skol2, skol3 ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := skol3
% 1.10/1.48 Y := X
% 1.10/1.48 Z := skol2
% 1.10/1.48 end
% 1.10/1.48 substitution1:
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 subsumption: (835) {G4,W9,D2,L3,V1,M2} R(794,16) { distinct_lines( X, skol3
% 1.10/1.48 ), apart_point_and_line( skol1, skol3 ), apart_point_and_line( skol2, X
% 1.10/1.48 ) }.
% 1.10/1.48 parent0: (1419) {G1,W9,D2,L3,V1,M3} { distinct_lines( X, skol3 ),
% 1.10/1.48 apart_point_and_line( skol2, X ), apart_point_and_line( skol1, skol3 )
% 1.10/1.48 }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := X
% 1.10/1.48 end
% 1.10/1.48 permutation0:
% 1.10/1.48 0 ==> 0
% 1.10/1.48 1 ==> 2
% 1.10/1.48 2 ==> 1
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 resolution: (1420) {G5,W14,D3,L4,V2,M4} { distinct_lines( line_connecting
% 1.10/1.48 ( skol1, X ), skol3 ), ! distinct_points( skol1, X ), distinct_lines( Y,
% 1.10/1.48 skol3 ), apart_point_and_line( skol2, Y ) }.
% 1.10/1.48 parent0[2]: (829) {G4,W11,D3,L3,V3,M1} R(794,116) { distinct_lines(
% 1.10/1.48 line_connecting( X, Y ), Z ), ! distinct_points( X, Y ), !
% 1.10/1.48 apart_point_and_line( X, Z ) }.
% 1.10/1.48 parent1[1]: (835) {G4,W9,D2,L3,V1,M2} R(794,16) { distinct_lines( X, skol3
% 1.10/1.48 ), apart_point_and_line( skol1, skol3 ), apart_point_and_line( skol2, X
% 1.10/1.48 ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := skol1
% 1.10/1.48 Y := X
% 1.10/1.48 Z := skol3
% 1.10/1.48 end
% 1.10/1.48 substitution1:
% 1.10/1.48 X := Y
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 subsumption: (992) {G5,W14,D3,L4,V2,M1} R(829,835) { ! distinct_points(
% 1.10/1.48 skol1, X ), distinct_lines( line_connecting( skol1, X ), skol3 ),
% 1.10/1.48 distinct_lines( Y, skol3 ), apart_point_and_line( skol2, Y ) }.
% 1.10/1.48 parent0: (1420) {G5,W14,D3,L4,V2,M4} { distinct_lines( line_connecting(
% 1.10/1.48 skol1, X ), skol3 ), ! distinct_points( skol1, X ), distinct_lines( Y,
% 1.10/1.48 skol3 ), apart_point_and_line( skol2, Y ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := X
% 1.10/1.48 Y := Y
% 1.10/1.48 end
% 1.10/1.48 permutation0:
% 1.10/1.48 0 ==> 1
% 1.10/1.48 1 ==> 0
% 1.10/1.48 2 ==> 2
% 1.10/1.48 3 ==> 3
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 factor: (1423) {G5,W13,D3,L3,V1,M3} { ! distinct_points( skol1, X ),
% 1.10/1.48 distinct_lines( line_connecting( skol1, X ), skol3 ),
% 1.10/1.48 apart_point_and_line( skol2, line_connecting( skol1, X ) ) }.
% 1.10/1.48 parent0[1, 2]: (992) {G5,W14,D3,L4,V2,M1} R(829,835) { ! distinct_points(
% 1.10/1.48 skol1, X ), distinct_lines( line_connecting( skol1, X ), skol3 ),
% 1.10/1.48 distinct_lines( Y, skol3 ), apart_point_and_line( skol2, Y ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := X
% 1.10/1.48 Y := line_connecting( skol1, X )
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 subsumption: (1008) {G6,W13,D3,L3,V1,M1} F(992) { ! distinct_points( skol1
% 1.10/1.48 , X ), distinct_lines( line_connecting( skol1, X ), skol3 ),
% 1.10/1.48 apart_point_and_line( skol2, line_connecting( skol1, X ) ) }.
% 1.10/1.48 parent0: (1423) {G5,W13,D3,L3,V1,M3} { ! distinct_points( skol1, X ),
% 1.10/1.48 distinct_lines( line_connecting( skol1, X ), skol3 ),
% 1.10/1.48 apart_point_and_line( skol2, line_connecting( skol1, X ) ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := X
% 1.10/1.48 end
% 1.10/1.48 permutation0:
% 1.10/1.48 0 ==> 0
% 1.10/1.48 1 ==> 1
% 1.10/1.48 2 ==> 2
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 resolution: (1424) {G3,W11,D3,L3,V0,M3} { ! distinct_points( skol1, skol2
% 1.10/1.48 ), ! distinct_points( skol1, skol2 ), distinct_lines( line_connecting(
% 1.10/1.48 skol1, skol2 ), skol3 ) }.
% 1.10/1.48 parent0[1]: (117) {G2,W8,D3,L2,V2,M1} F(114);r(0) { ! distinct_points( Y, X
% 1.10/1.48 ), ! apart_point_and_line( X, line_connecting( Y, X ) ) }.
% 1.10/1.48 parent1[2]: (1008) {G6,W13,D3,L3,V1,M1} F(992) { ! distinct_points( skol1,
% 1.10/1.48 X ), distinct_lines( line_connecting( skol1, X ), skol3 ),
% 1.10/1.48 apart_point_and_line( skol2, line_connecting( skol1, X ) ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 X := skol2
% 1.10/1.48 Y := skol1
% 1.10/1.48 end
% 1.10/1.48 substitution1:
% 1.10/1.48 X := skol2
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 factor: (1425) {G3,W8,D3,L2,V0,M2} { ! distinct_points( skol1, skol2 ),
% 1.10/1.48 distinct_lines( line_connecting( skol1, skol2 ), skol3 ) }.
% 1.10/1.48 parent0[0, 1]: (1424) {G3,W11,D3,L3,V0,M3} { ! distinct_points( skol1,
% 1.10/1.48 skol2 ), ! distinct_points( skol1, skol2 ), distinct_lines(
% 1.10/1.48 line_connecting( skol1, skol2 ), skol3 ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 resolution: (1427) {G1,W5,D3,L1,V0,M1} { distinct_lines( line_connecting(
% 1.10/1.48 skol1, skol2 ), skol3 ) }.
% 1.10/1.48 parent0[0]: (1425) {G3,W8,D3,L2,V0,M2} { ! distinct_points( skol1, skol2 )
% 1.10/1.48 , distinct_lines( line_connecting( skol1, skol2 ), skol3 ) }.
% 1.10/1.48 parent1[0]: (14) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol1, skol2 )
% 1.10/1.48 }.
% 1.10/1.48 substitution0:
% 1.10/1.48 end
% 1.10/1.48 substitution1:
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 subsumption: (1309) {G7,W5,D3,L1,V0,M1} R(1008,117);f;r(14) {
% 1.10/1.48 distinct_lines( line_connecting( skol1, skol2 ), skol3 ) }.
% 1.10/1.48 parent0: (1427) {G1,W5,D3,L1,V0,M1} { distinct_lines( line_connecting(
% 1.10/1.48 skol1, skol2 ), skol3 ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 end
% 1.10/1.48 permutation0:
% 1.10/1.48 0 ==> 0
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 resolution: (1428) {G3,W0,D0,L0,V0,M0} { }.
% 1.10/1.48 parent0[0]: (35) {G2,W5,D3,L1,V0,M1} R(31,17) { ! distinct_lines(
% 1.10/1.48 line_connecting( skol1, skol2 ), skol3 ) }.
% 1.10/1.48 parent1[0]: (1309) {G7,W5,D3,L1,V0,M1} R(1008,117);f;r(14) { distinct_lines
% 1.10/1.48 ( line_connecting( skol1, skol2 ), skol3 ) }.
% 1.10/1.48 substitution0:
% 1.10/1.48 end
% 1.10/1.48 substitution1:
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 subsumption: (1311) {G8,W0,D0,L0,V0,M0} S(1309);r(35) { }.
% 1.10/1.48 parent0: (1428) {G3,W0,D0,L0,V0,M0} { }.
% 1.10/1.48 substitution0:
% 1.10/1.48 end
% 1.10/1.48 permutation0:
% 1.10/1.48 end
% 1.10/1.48
% 1.10/1.48 Proof check complete!
% 1.10/1.48
% 1.10/1.48 Memory use:
% 1.10/1.48
% 1.10/1.48 space for terms: 18794
% 1.10/1.48 space for clauses: 46317
% 1.10/1.48
% 1.10/1.48
% 1.10/1.48 clauses generated: 41493
% 1.10/1.48 clauses kept: 1312
% 1.10/1.48 clauses selected: 469
% 1.10/1.48 clauses deleted: 5
% 1.10/1.48 clauses inuse deleted: 0
% 1.10/1.48
% 1.10/1.48 subsentry: 226517
% 1.10/1.48 literals s-matched: 126624
% 1.10/1.48 literals matched: 126596
% 1.10/1.48 full subsumption: 98737
% 1.10/1.48
% 1.10/1.48 checksum: 1067069966
% 1.10/1.48
% 1.10/1.48
% 1.10/1.48 Bliksem ended
%------------------------------------------------------------------------------