TSTP Solution File: GEO181+2 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO181+2 : 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 02:52:21 EDT 2022
% Result : Theorem 1.33s 1.71s
% Output : Refutation 1.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO181+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n022.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 10:58:17 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.33/1.71 *** allocated 10000 integers for termspace/termends
% 1.33/1.71 *** allocated 10000 integers for clauses
% 1.33/1.71 *** allocated 10000 integers for justifications
% 1.33/1.71 Bliksem 1.12
% 1.33/1.71
% 1.33/1.71
% 1.33/1.71 Automatic Strategy Selection
% 1.33/1.71
% 1.33/1.71
% 1.33/1.71 Clauses:
% 1.33/1.71
% 1.33/1.71 { ! distinct_points( X, X ) }.
% 1.33/1.71 { ! distinct_lines( X, X ) }.
% 1.33/1.71 { ! convergent_lines( X, X ) }.
% 1.33/1.71 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 1.33/1.71 ) }.
% 1.33/1.71 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 1.33/1.71 }.
% 1.33/1.71 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 1.33/1.71 , Z ) }.
% 1.33/1.71 { ! distinct_points( X, Y ), ! apart_point_and_line( Z, line_connecting( X
% 1.33/1.71 , Y ) ), distinct_points( Z, X ) }.
% 1.33/1.71 { ! distinct_points( X, Y ), ! apart_point_and_line( Z, line_connecting( X
% 1.33/1.71 , Y ) ), distinct_points( Z, Y ) }.
% 1.33/1.71 { ! convergent_lines( X, Y ), ! apart_point_and_line( Z, X ),
% 1.33/1.71 distinct_points( Z, intersection_point( X, Y ) ) }.
% 1.33/1.71 { ! convergent_lines( X, Y ), ! apart_point_and_line( Z, Y ),
% 1.33/1.71 distinct_points( Z, intersection_point( X, Y ) ) }.
% 1.33/1.71 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 1.33/1.71 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 1.33/1.71 apart_point_and_line( Y, T ) }.
% 1.33/1.71 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 1.33/1.71 apart_point_and_line( Z, Y ) }.
% 1.33/1.71 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 1.33/1.71 apart_point_and_line( X, Z ) }.
% 1.33/1.71 { ! convergent_lines( X, Y ), distinct_lines( X, Y ) }.
% 1.33/1.71 { distinct_points( skol1, skol2 ) }.
% 1.33/1.71 { apart_point_and_line( skol3, line_connecting( skol1, skol2 ) ) }.
% 1.33/1.71 { ! apart_point_and_line( skol2, line_connecting( skol1, skol3 ) ) }.
% 1.33/1.71
% 1.33/1.71 percentage equality = 0.000000, percentage horn = 0.647059
% 1.33/1.71 This a non-horn, non-equality problem
% 1.33/1.71
% 1.33/1.71
% 1.33/1.71 Options Used:
% 1.33/1.71
% 1.33/1.71 useres = 1
% 1.33/1.71 useparamod = 0
% 1.33/1.71 useeqrefl = 0
% 1.33/1.71 useeqfact = 0
% 1.33/1.71 usefactor = 1
% 1.33/1.71 usesimpsplitting = 0
% 1.33/1.71 usesimpdemod = 0
% 1.33/1.71 usesimpres = 3
% 1.33/1.71
% 1.33/1.71 resimpinuse = 1000
% 1.33/1.71 resimpclauses = 20000
% 1.33/1.71 substype = standard
% 1.33/1.71 backwardsubs = 1
% 1.33/1.71 selectoldest = 5
% 1.33/1.71
% 1.33/1.71 litorderings [0] = split
% 1.33/1.71 litorderings [1] = liftord
% 1.33/1.71
% 1.33/1.71 termordering = none
% 1.33/1.71
% 1.33/1.71 litapriori = 1
% 1.33/1.71 termapriori = 0
% 1.33/1.71 litaposteriori = 0
% 1.33/1.71 termaposteriori = 0
% 1.33/1.71 demodaposteriori = 0
% 1.33/1.71 ordereqreflfact = 0
% 1.33/1.71
% 1.33/1.71 litselect = none
% 1.33/1.71
% 1.33/1.71 maxweight = 15
% 1.33/1.71 maxdepth = 30000
% 1.33/1.71 maxlength = 115
% 1.33/1.71 maxnrvars = 195
% 1.33/1.71 excuselevel = 1
% 1.33/1.71 increasemaxweight = 1
% 1.33/1.71
% 1.33/1.71 maxselected = 10000000
% 1.33/1.71 maxnrclauses = 10000000
% 1.33/1.71
% 1.33/1.71 showgenerated = 0
% 1.33/1.71 showkept = 0
% 1.33/1.71 showselected = 0
% 1.33/1.71 showdeleted = 0
% 1.33/1.71 showresimp = 1
% 1.33/1.71 showstatus = 2000
% 1.33/1.71
% 1.33/1.71 prologoutput = 0
% 1.33/1.71 nrgoals = 5000000
% 1.33/1.71 totalproof = 1
% 1.33/1.71
% 1.33/1.71 Symbols occurring in the translation:
% 1.33/1.71
% 1.33/1.71 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.33/1.71 . [1, 2] (w:1, o:19, a:1, s:1, b:0),
% 1.33/1.71 ! [4, 1] (w:0, o:14, a:1, s:1, b:0),
% 1.33/1.71 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.33/1.71 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.33/1.71 distinct_points [36, 2] (w:1, o:44, a:1, s:1, b:0),
% 1.33/1.71 distinct_lines [37, 2] (w:1, o:45, a:1, s:1, b:0),
% 1.33/1.71 convergent_lines [38, 2] (w:1, o:43, a:1, s:1, b:0),
% 1.33/1.71 line_connecting [41, 2] (w:1, o:46, a:1, s:1, b:0),
% 1.33/1.71 apart_point_and_line [42, 2] (w:1, o:47, a:1, s:1, b:0),
% 1.33/1.71 intersection_point [43, 2] (w:1, o:48, a:1, s:1, b:0),
% 1.33/1.71 skol1 [46, 0] (w:1, o:11, a:1, s:1, b:0),
% 1.33/1.71 skol2 [47, 0] (w:1, o:12, a:1, s:1, b:0),
% 1.33/1.71 skol3 [48, 0] (w:1, o:13, a:1, s:1, b:0).
% 1.33/1.71
% 1.33/1.71
% 1.33/1.71 Starting Search:
% 1.33/1.71
% 1.33/1.71 *** allocated 15000 integers for clauses
% 1.33/1.71 *** allocated 22500 integers for clauses
% 1.33/1.71 *** allocated 33750 integers for clauses
% 1.33/1.71 *** allocated 15000 integers for termspace/termends
% 1.33/1.71 *** allocated 50625 integers for clauses
% 1.33/1.71
% 1.33/1.71 Bliksems!, er is een bewijs:
% 1.33/1.71 % SZS status Theorem
% 1.33/1.71 % SZS output start Refutation
% 1.33/1.71
% 1.33/1.71 (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 1.33/1.71 (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 1.33/1.71 (3) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ), distinct_points( Y, Z
% 1.33/1.71 ), ! distinct_points( X, Y ) }.
% 1.33/1.71 (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 1.33/1.71 , ! distinct_lines( X, Y ) }.
% 1.33/1.71 (6) {G0,W11,D3,L3,V3,M1} I { ! distinct_points( X, Y ), distinct_points( Z
% 1.33/1.71 , X ), ! apart_point_and_line( Z, line_connecting( X, Y ) ) }.
% 1.33/1.71 (7) {G0,W11,D3,L3,V3,M1} I { ! distinct_points( X, Y ), distinct_points( Z
% 1.33/1.71 , Y ), ! apart_point_and_line( Z, line_connecting( X, Y ) ) }.
% 1.33/1.71 (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! distinct_lines(
% 1.33/1.71 Z, T ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 1.33/1.71 apart_point_and_line( Y, T ), apart_point_and_line( X, Z ) }.
% 1.33/1.71 (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ), apart_point_and_line
% 1.33/1.71 ( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 1.33/1.71 (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), apart_point_and_line(
% 1.33/1.71 X, Z ), ! apart_point_and_line( X, Y ) }.
% 1.33/1.71 (14) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol1, skol2 ) }.
% 1.33/1.71 (15) {G0,W5,D3,L1,V0,M1} I { apart_point_and_line( skol3, line_connecting(
% 1.33/1.71 skol1, skol2 ) ) }.
% 1.33/1.71 (16) {G0,W5,D3,L1,V0,M1} I { ! apart_point_and_line( skol2, line_connecting
% 1.33/1.71 ( skol1, skol3 ) ) }.
% 1.33/1.71 (20) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ),
% 1.33/1.71 distinct_points( X, Y ) }.
% 1.33/1.71 (27) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 1.33/1.71 ( X, Y ) }.
% 1.33/1.71 (28) {G2,W9,D2,L3,V3,M3} R(27,4) { distinct_lines( Z, X ), ! distinct_lines
% 1.33/1.71 ( Y, Z ), distinct_lines( X, Y ) }.
% 1.33/1.71 (48) {G1,W3,D2,L1,V0,M1} R(6,15);r(14) { distinct_points( skol3, skol1 )
% 1.33/1.71 }.
% 1.33/1.71 (49) {G2,W3,D2,L1,V0,M1} R(48,20) { distinct_points( skol1, skol3 ) }.
% 1.33/1.71 (55) {G1,W3,D2,L1,V0,M1} R(7,15);r(14) { distinct_points( skol3, skol2 )
% 1.33/1.71 }.
% 1.33/1.71 (56) {G2,W3,D2,L1,V0,M1} R(55,20) { distinct_points( skol2, skol3 ) }.
% 1.33/1.71 (100) {G1,W19,D3,L5,V2,M3} R(10,16) { ! distinct_points( skol2, X ), !
% 1.33/1.71 distinct_lines( Y, line_connecting( skol1, skol3 ) ),
% 1.33/1.71 apart_point_and_line( X, line_connecting( skol1, skol3 ) ),
% 1.33/1.71 apart_point_and_line( skol2, Y ), apart_point_and_line( X, Y ) }.
% 1.33/1.71 (101) {G1,W19,D3,L5,V2,M3} R(10,16) { ! distinct_points( X, skol2 ), !
% 1.33/1.71 distinct_lines( line_connecting( skol1, skol3 ), Y ),
% 1.33/1.71 apart_point_and_line( skol2, Y ), apart_point_and_line( X,
% 1.33/1.71 line_connecting( skol1, skol3 ) ), apart_point_and_line( X, Y ) }.
% 1.33/1.71 (117) {G1,W14,D3,L4,V4,M1} R(11,7) { distinct_points( X, Y ), !
% 1.33/1.71 distinct_points( Z, T ), distinct_points( Y, T ), ! apart_point_and_line
% 1.33/1.71 ( X, line_connecting( Z, T ) ) }.
% 1.33/1.71 (118) {G1,W14,D3,L4,V4,M1} R(11,6) { distinct_points( X, Y ), !
% 1.33/1.71 distinct_points( Z, T ), distinct_points( Y, Z ), ! apart_point_and_line
% 1.33/1.71 ( X, line_connecting( Z, T ) ) }.
% 1.33/1.71 (121) {G2,W8,D3,L2,V2,M1} F(118);r(0) { ! distinct_points( X, Y ), !
% 1.33/1.71 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.33/1.71 (122) {G2,W8,D3,L2,V2,M1} F(117);r(0) { ! distinct_points( Y, X ), !
% 1.33/1.71 apart_point_and_line( X, line_connecting( Y, X ) ) }.
% 1.33/1.71 (139) {G1,W8,D3,L2,V1,M1} R(12,15) { distinct_lines( line_connecting( skol1
% 1.33/1.71 , skol2 ), X ), apart_point_and_line( skol3, X ) }.
% 1.33/1.71 (142) {G3,W10,D3,L2,V1,M1} R(139,121) { ! distinct_points( skol3, X ),
% 1.33/1.71 distinct_lines( line_connecting( skol1, skol2 ), line_connecting( skol3,
% 1.33/1.71 X ) ) }.
% 1.33/1.71 (325) {G4,W13,D3,L3,V2,M2} R(142,28) { ! distinct_points( skol3, X ),
% 1.33/1.71 distinct_lines( Y, line_connecting( skol1, skol2 ) ), distinct_lines(
% 1.33/1.71 line_connecting( skol3, X ), Y ) }.
% 1.33/1.71 (590) {G3,W14,D3,L4,V1,M1} R(100,122);r(56) { ! distinct_lines( X,
% 1.33/1.71 line_connecting( skol1, skol3 ) ), apart_point_and_line( skol2, X ), !
% 1.33/1.71 distinct_points( skol1, skol3 ), apart_point_and_line( skol3, X ) }.
% 1.33/1.71 (591) {G3,W14,D3,L4,V1,M1} R(101,121);r(14) { ! distinct_lines(
% 1.33/1.71 line_connecting( skol1, skol3 ), X ), apart_point_and_line( skol1, X ), !
% 1.33/1.71 distinct_points( skol1, skol3 ), apart_point_and_line( skol2, X ) }.
% 1.33/1.71 (593) {G4,W11,D3,L3,V1,M1} S(591);r(49) { ! distinct_lines( line_connecting
% 1.33/1.71 ( skol1, skol3 ), X ), apart_point_and_line( skol1, X ),
% 1.33/1.71 apart_point_and_line( skol2, X ) }.
% 1.33/1.71 (598) {G5,W15,D3,L3,V1,M1} R(593,122) { ! distinct_lines( line_connecting(
% 1.33/1.71 skol1, skol3 ), line_connecting( X, skol2 ) ), ! distinct_points( X,
% 1.33/1.71 skol2 ), apart_point_and_line( skol1, line_connecting( X, skol2 ) ) }.
% 1.33/1.71 (614) {G4,W11,D3,L3,V1,M1} S(590);r(49) { ! distinct_lines( X,
% 1.33/1.71 line_connecting( skol1, skol3 ) ), apart_point_and_line( skol2, X ),
% 1.33/1.71 apart_point_and_line( skol3, X ) }.
% 1.33/1.71 (618) {G5,W15,D3,L3,V1,M1} R(614,121) { ! distinct_lines( line_connecting(
% 1.33/1.71 skol3, X ), line_connecting( skol1, skol3 ) ), ! distinct_points( skol3,
% 1.33/1.71 X ), apart_point_and_line( skol2, line_connecting( skol3, X ) ) }.
% 1.33/1.71 (622) {G6,W7,D3,L1,V0,M1} R(618,122);f;r(55) { ! distinct_lines(
% 1.33/1.71 line_connecting( skol3, skol2 ), line_connecting( skol1, skol3 ) ) }.
% 1.33/1.71 (625) {G7,W7,D3,L1,V0,M1} R(622,325);r(55) { distinct_lines(
% 1.33/1.71 line_connecting( skol1, skol3 ), line_connecting( skol1, skol2 ) ) }.
% 1.33/1.71 (870) {G8,W3,D2,L1,V0,M1} R(598,121);f;r(625) { ! distinct_points( skol1,
% 1.33/1.71 skol2 ) }.
% 1.33/1.71 (873) {G9,W0,D0,L0,V0,M0} S(870);r(14) { }.
% 1.33/1.71
% 1.33/1.71
% 1.33/1.71 % SZS output end Refutation
% 1.33/1.71 found a proof!
% 1.33/1.71
% 1.33/1.71
% 1.33/1.71 Unprocessed initial clauses:
% 1.33/1.71
% 1.33/1.71 (875) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 1.33/1.71 (876) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 1.33/1.71 (877) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 1.33/1.71 (878) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 1.33/1.71 , Z ), distinct_points( Y, Z ) }.
% 1.33/1.71 (879) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X, Z
% 1.33/1.71 ), distinct_lines( Y, Z ) }.
% 1.33/1.71 (880) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines(
% 1.33/1.71 X, Z ), convergent_lines( Y, Z ) }.
% 1.33/1.71 (881) {G0,W11,D3,L3,V3,M3} { ! distinct_points( X, Y ), !
% 1.33/1.71 apart_point_and_line( Z, line_connecting( X, Y ) ), distinct_points( Z, X
% 1.33/1.71 ) }.
% 1.33/1.71 (882) {G0,W11,D3,L3,V3,M3} { ! distinct_points( X, Y ), !
% 1.33/1.71 apart_point_and_line( Z, line_connecting( X, Y ) ), distinct_points( Z, Y
% 1.33/1.71 ) }.
% 1.33/1.71 (883) {G0,W11,D3,L3,V3,M3} { ! convergent_lines( X, Y ), !
% 1.33/1.71 apart_point_and_line( Z, X ), distinct_points( Z, intersection_point( X,
% 1.33/1.71 Y ) ) }.
% 1.33/1.71 (884) {G0,W11,D3,L3,V3,M3} { ! convergent_lines( X, Y ), !
% 1.33/1.71 apart_point_and_line( Z, Y ), distinct_points( Z, intersection_point( X,
% 1.33/1.71 Y ) ) }.
% 1.33/1.71 (885) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines(
% 1.33/1.71 Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 1.33/1.71 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 1.33/1.71 (886) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 1.33/1.71 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 1.33/1.71 (887) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ), distinct_lines
% 1.33/1.71 ( Y, Z ), apart_point_and_line( X, Z ) }.
% 1.33/1.71 (888) {G0,W6,D2,L2,V2,M2} { ! convergent_lines( X, Y ), distinct_lines( X
% 1.33/1.71 , Y ) }.
% 1.33/1.71 (889) {G0,W3,D2,L1,V0,M1} { distinct_points( skol1, skol2 ) }.
% 1.33/1.71 (890) {G0,W5,D3,L1,V0,M1} { apart_point_and_line( skol3, line_connecting(
% 1.33/1.71 skol1, skol2 ) ) }.
% 1.33/1.71 (891) {G0,W5,D3,L1,V0,M1} { ! apart_point_and_line( skol2, line_connecting
% 1.33/1.71 ( skol1, skol3 ) ) }.
% 1.33/1.71
% 1.33/1.71
% 1.33/1.71 Total Proof:
% 1.33/1.71
% 1.33/1.71 subsumption: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 1.33/1.71 parent0: (875) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := X
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 0
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 1.33/1.71 parent0: (876) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := X
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 0
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (3) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ),
% 1.33/1.71 distinct_points( Y, Z ), ! distinct_points( X, Y ) }.
% 1.33/1.71 parent0: (878) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ),
% 1.33/1.71 distinct_points( X, Z ), distinct_points( Y, Z ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := X
% 1.33/1.71 Y := Y
% 1.33/1.71 Z := Z
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 2
% 1.33/1.71 1 ==> 0
% 1.33/1.71 2 ==> 1
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 1.33/1.71 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 1.33/1.71 parent0: (879) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ),
% 1.33/1.71 distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := X
% 1.33/1.71 Y := Y
% 1.33/1.71 Z := Z
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 2
% 1.33/1.71 1 ==> 0
% 1.33/1.71 2 ==> 1
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (6) {G0,W11,D3,L3,V3,M1} I { ! distinct_points( X, Y ),
% 1.33/1.71 distinct_points( Z, X ), ! apart_point_and_line( Z, line_connecting( X, Y
% 1.33/1.71 ) ) }.
% 1.33/1.71 parent0: (881) {G0,W11,D3,L3,V3,M3} { ! distinct_points( X, Y ), !
% 1.33/1.71 apart_point_and_line( Z, line_connecting( X, Y ) ), distinct_points( Z, X
% 1.33/1.71 ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := X
% 1.33/1.71 Y := Y
% 1.33/1.71 Z := Z
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 0
% 1.33/1.71 1 ==> 2
% 1.33/1.71 2 ==> 1
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (7) {G0,W11,D3,L3,V3,M1} I { ! distinct_points( X, Y ),
% 1.33/1.71 distinct_points( Z, Y ), ! apart_point_and_line( Z, line_connecting( X, Y
% 1.33/1.71 ) ) }.
% 1.33/1.71 parent0: (882) {G0,W11,D3,L3,V3,M3} { ! distinct_points( X, Y ), !
% 1.33/1.71 apart_point_and_line( Z, line_connecting( X, Y ) ), distinct_points( Z, Y
% 1.33/1.71 ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := X
% 1.33/1.71 Y := Y
% 1.33/1.71 Z := Z
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 0
% 1.33/1.71 1 ==> 2
% 1.33/1.71 2 ==> 1
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), !
% 1.33/1.71 distinct_lines( Z, T ), apart_point_and_line( X, T ),
% 1.33/1.71 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ),
% 1.33/1.71 apart_point_and_line( X, Z ) }.
% 1.33/1.71 parent0: (885) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), !
% 1.33/1.71 distinct_lines( Z, T ), apart_point_and_line( X, Z ),
% 1.33/1.71 apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 1.33/1.71 apart_point_and_line( Y, T ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := X
% 1.33/1.71 Y := Y
% 1.33/1.71 Z := Z
% 1.33/1.71 T := T
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 0
% 1.33/1.71 1 ==> 1
% 1.33/1.71 2 ==> 5
% 1.33/1.71 3 ==> 2
% 1.33/1.71 4 ==> 3
% 1.33/1.71 5 ==> 4
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ),
% 1.33/1.71 apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 1.33/1.71 parent0: (886) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 1.33/1.71 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := X
% 1.33/1.71 Y := Y
% 1.33/1.71 Z := Z
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 2
% 1.33/1.71 1 ==> 0
% 1.33/1.71 2 ==> 1
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 1.33/1.71 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 1.33/1.71 parent0: (887) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 1.33/1.71 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := X
% 1.33/1.71 Y := Y
% 1.33/1.71 Z := Z
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 2
% 1.33/1.71 1 ==> 0
% 1.33/1.71 2 ==> 1
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (14) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol1, skol2 )
% 1.33/1.71 }.
% 1.33/1.71 parent0: (889) {G0,W3,D2,L1,V0,M1} { distinct_points( skol1, skol2 ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 0
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (15) {G0,W5,D3,L1,V0,M1} I { apart_point_and_line( skol3,
% 1.33/1.71 line_connecting( skol1, skol2 ) ) }.
% 1.33/1.71 parent0: (890) {G0,W5,D3,L1,V0,M1} { apart_point_and_line( skol3,
% 1.33/1.71 line_connecting( skol1, skol2 ) ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 0
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (16) {G0,W5,D3,L1,V0,M1} I { ! apart_point_and_line( skol2,
% 1.33/1.71 line_connecting( skol1, skol3 ) ) }.
% 1.33/1.71 parent0: (891) {G0,W5,D3,L1,V0,M1} { ! apart_point_and_line( skol2,
% 1.33/1.71 line_connecting( skol1, skol3 ) ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 0
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 resolution: (955) {G1,W6,D2,L2,V2,M2} { distinct_points( Y, X ), !
% 1.33/1.71 distinct_points( X, Y ) }.
% 1.33/1.71 parent0[0]: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 1.33/1.71 parent1[0]: (3) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ),
% 1.33/1.71 distinct_points( Y, Z ), ! distinct_points( X, Y ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := X
% 1.33/1.71 end
% 1.33/1.71 substitution1:
% 1.33/1.71 X := X
% 1.33/1.71 Y := Y
% 1.33/1.71 Z := X
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (20) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ),
% 1.33/1.71 distinct_points( X, Y ) }.
% 1.33/1.71 parent0: (955) {G1,W6,D2,L2,V2,M2} { distinct_points( Y, X ), !
% 1.33/1.71 distinct_points( X, Y ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := Y
% 1.33/1.71 Y := X
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 1
% 1.33/1.71 1 ==> 0
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 resolution: (957) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 1.33/1.71 distinct_lines( X, Y ) }.
% 1.33/1.71 parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 1.33/1.71 parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 1.33/1.71 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := X
% 1.33/1.71 end
% 1.33/1.71 substitution1:
% 1.33/1.71 X := X
% 1.33/1.71 Y := Y
% 1.33/1.71 Z := X
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (27) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 1.33/1.71 distinct_lines( X, Y ) }.
% 1.33/1.71 parent0: (957) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 1.33/1.71 distinct_lines( X, Y ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := Y
% 1.33/1.71 Y := X
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 1
% 1.33/1.71 1 ==> 0
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 resolution: (959) {G1,W9,D2,L3,V3,M3} { distinct_lines( Y, X ),
% 1.33/1.71 distinct_lines( Z, Y ), ! distinct_lines( X, Z ) }.
% 1.33/1.71 parent0[0]: (27) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 1.33/1.71 distinct_lines( X, Y ) }.
% 1.33/1.71 parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 1.33/1.71 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := Y
% 1.33/1.71 Y := X
% 1.33/1.71 end
% 1.33/1.71 substitution1:
% 1.33/1.71 X := X
% 1.33/1.71 Y := Z
% 1.33/1.71 Z := Y
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (28) {G2,W9,D2,L3,V3,M3} R(27,4) { distinct_lines( Z, X ), !
% 1.33/1.71 distinct_lines( Y, Z ), distinct_lines( X, Y ) }.
% 1.33/1.71 parent0: (959) {G1,W9,D2,L3,V3,M3} { distinct_lines( Y, X ),
% 1.33/1.71 distinct_lines( Z, Y ), ! distinct_lines( X, Z ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := Y
% 1.33/1.71 Y := X
% 1.33/1.71 Z := Z
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 2
% 1.33/1.71 1 ==> 0
% 1.33/1.71 2 ==> 1
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 resolution: (962) {G1,W6,D2,L2,V0,M2} { ! distinct_points( skol1, skol2 )
% 1.33/1.71 , distinct_points( skol3, skol1 ) }.
% 1.33/1.71 parent0[2]: (6) {G0,W11,D3,L3,V3,M1} I { ! distinct_points( X, Y ),
% 1.33/1.71 distinct_points( Z, X ), ! apart_point_and_line( Z, line_connecting( X, Y
% 1.33/1.71 ) ) }.
% 1.33/1.71 parent1[0]: (15) {G0,W5,D3,L1,V0,M1} I { apart_point_and_line( skol3,
% 1.33/1.71 line_connecting( skol1, skol2 ) ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := skol1
% 1.33/1.71 Y := skol2
% 1.33/1.71 Z := skol3
% 1.33/1.71 end
% 1.33/1.71 substitution1:
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 resolution: (963) {G1,W3,D2,L1,V0,M1} { distinct_points( skol3, skol1 )
% 1.33/1.71 }.
% 1.33/1.71 parent0[0]: (962) {G1,W6,D2,L2,V0,M2} { ! distinct_points( skol1, skol2 )
% 1.33/1.71 , distinct_points( skol3, skol1 ) }.
% 1.33/1.71 parent1[0]: (14) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol1, skol2 )
% 1.33/1.71 }.
% 1.33/1.71 substitution0:
% 1.33/1.71 end
% 1.33/1.71 substitution1:
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (48) {G1,W3,D2,L1,V0,M1} R(6,15);r(14) { distinct_points(
% 1.33/1.71 skol3, skol1 ) }.
% 1.33/1.71 parent0: (963) {G1,W3,D2,L1,V0,M1} { distinct_points( skol3, skol1 ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 0
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 resolution: (964) {G2,W3,D2,L1,V0,M1} { distinct_points( skol1, skol3 )
% 1.33/1.71 }.
% 1.33/1.71 parent0[0]: (20) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ),
% 1.33/1.71 distinct_points( X, Y ) }.
% 1.33/1.71 parent1[0]: (48) {G1,W3,D2,L1,V0,M1} R(6,15);r(14) { distinct_points( skol3
% 1.33/1.71 , skol1 ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := skol1
% 1.33/1.71 Y := skol3
% 1.33/1.71 end
% 1.33/1.71 substitution1:
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (49) {G2,W3,D2,L1,V0,M1} R(48,20) { distinct_points( skol1,
% 1.33/1.71 skol3 ) }.
% 1.33/1.71 parent0: (964) {G2,W3,D2,L1,V0,M1} { distinct_points( skol1, skol3 ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 0
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 resolution: (965) {G1,W6,D2,L2,V0,M2} { ! distinct_points( skol1, skol2 )
% 1.33/1.71 , distinct_points( skol3, skol2 ) }.
% 1.33/1.71 parent0[2]: (7) {G0,W11,D3,L3,V3,M1} I { ! distinct_points( X, Y ),
% 1.33/1.71 distinct_points( Z, Y ), ! apart_point_and_line( Z, line_connecting( X, Y
% 1.33/1.71 ) ) }.
% 1.33/1.71 parent1[0]: (15) {G0,W5,D3,L1,V0,M1} I { apart_point_and_line( skol3,
% 1.33/1.71 line_connecting( skol1, skol2 ) ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := skol1
% 1.33/1.71 Y := skol2
% 1.33/1.71 Z := skol3
% 1.33/1.71 end
% 1.33/1.71 substitution1:
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 resolution: (966) {G1,W3,D2,L1,V0,M1} { distinct_points( skol3, skol2 )
% 1.33/1.71 }.
% 1.33/1.71 parent0[0]: (965) {G1,W6,D2,L2,V0,M2} { ! distinct_points( skol1, skol2 )
% 1.33/1.71 , distinct_points( skol3, skol2 ) }.
% 1.33/1.71 parent1[0]: (14) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol1, skol2 )
% 1.33/1.71 }.
% 1.33/1.71 substitution0:
% 1.33/1.71 end
% 1.33/1.71 substitution1:
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (55) {G1,W3,D2,L1,V0,M1} R(7,15);r(14) { distinct_points(
% 1.33/1.71 skol3, skol2 ) }.
% 1.33/1.71 parent0: (966) {G1,W3,D2,L1,V0,M1} { distinct_points( skol3, skol2 ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 0
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 resolution: (967) {G2,W3,D2,L1,V0,M1} { distinct_points( skol2, skol3 )
% 1.33/1.71 }.
% 1.33/1.71 parent0[0]: (20) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ),
% 1.33/1.71 distinct_points( X, Y ) }.
% 1.33/1.71 parent1[0]: (55) {G1,W3,D2,L1,V0,M1} R(7,15);r(14) { distinct_points( skol3
% 1.33/1.71 , skol2 ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := skol2
% 1.33/1.71 Y := skol3
% 1.33/1.71 end
% 1.33/1.71 substitution1:
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (56) {G2,W3,D2,L1,V0,M1} R(55,20) { distinct_points( skol2,
% 1.33/1.71 skol3 ) }.
% 1.33/1.71 parent0: (967) {G2,W3,D2,L1,V0,M1} { distinct_points( skol2, skol3 ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 0
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 resolution: (968) {G1,W19,D3,L5,V2,M5} { ! distinct_points( skol2, X ), !
% 1.33/1.71 distinct_lines( Y, line_connecting( skol1, skol3 ) ),
% 1.33/1.71 apart_point_and_line( X, Y ), apart_point_and_line( X, line_connecting(
% 1.33/1.71 skol1, skol3 ) ), apart_point_and_line( skol2, Y ) }.
% 1.33/1.71 parent0[0]: (16) {G0,W5,D3,L1,V0,M1} I { ! apart_point_and_line( skol2,
% 1.33/1.71 line_connecting( skol1, skol3 ) ) }.
% 1.33/1.71 parent1[2]: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), !
% 1.33/1.71 distinct_lines( Z, T ), apart_point_and_line( X, T ),
% 1.33/1.71 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ),
% 1.33/1.71 apart_point_and_line( X, Z ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 end
% 1.33/1.71 substitution1:
% 1.33/1.71 X := skol2
% 1.33/1.71 Y := X
% 1.33/1.71 Z := Y
% 1.33/1.71 T := line_connecting( skol1, skol3 )
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (100) {G1,W19,D3,L5,V2,M3} R(10,16) { ! distinct_points( skol2
% 1.33/1.71 , X ), ! distinct_lines( Y, line_connecting( skol1, skol3 ) ),
% 1.33/1.71 apart_point_and_line( X, line_connecting( skol1, skol3 ) ),
% 1.33/1.71 apart_point_and_line( skol2, Y ), apart_point_and_line( X, Y ) }.
% 1.33/1.71 parent0: (968) {G1,W19,D3,L5,V2,M5} { ! distinct_points( skol2, X ), !
% 1.33/1.71 distinct_lines( Y, line_connecting( skol1, skol3 ) ),
% 1.33/1.71 apart_point_and_line( X, Y ), apart_point_and_line( X, line_connecting(
% 1.33/1.71 skol1, skol3 ) ), apart_point_and_line( skol2, Y ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := X
% 1.33/1.71 Y := Y
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 0
% 1.33/1.71 1 ==> 1
% 1.33/1.71 2 ==> 4
% 1.33/1.71 3 ==> 2
% 1.33/1.71 4 ==> 3
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 resolution: (978) {G1,W19,D3,L5,V2,M5} { ! distinct_points( X, skol2 ), !
% 1.33/1.71 distinct_lines( line_connecting( skol1, skol3 ), Y ),
% 1.33/1.71 apart_point_and_line( X, Y ), apart_point_and_line( skol2, Y ),
% 1.33/1.71 apart_point_and_line( X, line_connecting( skol1, skol3 ) ) }.
% 1.33/1.71 parent0[0]: (16) {G0,W5,D3,L1,V0,M1} I { ! apart_point_and_line( skol2,
% 1.33/1.71 line_connecting( skol1, skol3 ) ) }.
% 1.33/1.71 parent1[3]: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), !
% 1.33/1.71 distinct_lines( Z, T ), apart_point_and_line( X, T ),
% 1.33/1.71 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ),
% 1.33/1.71 apart_point_and_line( X, Z ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 end
% 1.33/1.71 substitution1:
% 1.33/1.71 X := X
% 1.33/1.71 Y := skol2
% 1.33/1.71 Z := line_connecting( skol1, skol3 )
% 1.33/1.71 T := Y
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (101) {G1,W19,D3,L5,V2,M3} R(10,16) { ! distinct_points( X,
% 1.33/1.71 skol2 ), ! distinct_lines( line_connecting( skol1, skol3 ), Y ),
% 1.33/1.71 apart_point_and_line( skol2, Y ), apart_point_and_line( X,
% 1.33/1.71 line_connecting( skol1, skol3 ) ), apart_point_and_line( X, Y ) }.
% 1.33/1.71 parent0: (978) {G1,W19,D3,L5,V2,M5} { ! distinct_points( X, skol2 ), !
% 1.33/1.71 distinct_lines( line_connecting( skol1, skol3 ), Y ),
% 1.33/1.71 apart_point_and_line( X, Y ), apart_point_and_line( skol2, Y ),
% 1.33/1.71 apart_point_and_line( X, line_connecting( skol1, skol3 ) ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := X
% 1.33/1.71 Y := Y
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 0
% 1.33/1.71 1 ==> 1
% 1.33/1.71 2 ==> 4
% 1.33/1.71 3 ==> 2
% 1.33/1.71 4 ==> 3
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 resolution: (987) {G1,W14,D3,L4,V4,M4} { ! distinct_points( X, Y ),
% 1.33/1.71 distinct_points( Z, Y ), distinct_points( T, Z ), ! apart_point_and_line
% 1.33/1.71 ( T, line_connecting( X, Y ) ) }.
% 1.33/1.71 parent0[2]: (7) {G0,W11,D3,L3,V3,M1} I { ! distinct_points( X, Y ),
% 1.33/1.71 distinct_points( Z, Y ), ! apart_point_and_line( Z, line_connecting( X, Y
% 1.33/1.71 ) ) }.
% 1.33/1.71 parent1[1]: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ),
% 1.33/1.71 apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := X
% 1.33/1.71 Y := Y
% 1.33/1.71 Z := Z
% 1.33/1.71 end
% 1.33/1.71 substitution1:
% 1.33/1.71 X := T
% 1.33/1.71 Y := line_connecting( X, Y )
% 1.33/1.71 Z := Z
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (117) {G1,W14,D3,L4,V4,M1} R(11,7) { distinct_points( X, Y ),
% 1.33/1.71 ! distinct_points( Z, T ), distinct_points( Y, T ), !
% 1.33/1.71 apart_point_and_line( X, line_connecting( Z, T ) ) }.
% 1.33/1.71 parent0: (987) {G1,W14,D3,L4,V4,M4} { ! distinct_points( X, Y ),
% 1.33/1.71 distinct_points( Z, Y ), distinct_points( T, Z ), ! apart_point_and_line
% 1.33/1.71 ( T, line_connecting( X, Y ) ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := Z
% 1.33/1.71 Y := T
% 1.33/1.71 Z := Y
% 1.33/1.71 T := X
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 1
% 1.33/1.71 1 ==> 2
% 1.33/1.71 2 ==> 0
% 1.33/1.71 3 ==> 3
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 resolution: (991) {G1,W14,D3,L4,V4,M4} { ! distinct_points( X, Y ),
% 1.33/1.71 distinct_points( Z, X ), distinct_points( T, Z ), ! apart_point_and_line
% 1.33/1.71 ( T, line_connecting( X, Y ) ) }.
% 1.33/1.71 parent0[2]: (6) {G0,W11,D3,L3,V3,M1} I { ! distinct_points( X, Y ),
% 1.33/1.71 distinct_points( Z, X ), ! apart_point_and_line( Z, line_connecting( X, Y
% 1.33/1.71 ) ) }.
% 1.33/1.71 parent1[1]: (11) {G0,W9,D2,L3,V3,M2} I { distinct_points( X, Z ),
% 1.33/1.71 apart_point_and_line( Z, Y ), ! apart_point_and_line( X, Y ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := X
% 1.33/1.71 Y := Y
% 1.33/1.71 Z := Z
% 1.33/1.71 end
% 1.33/1.71 substitution1:
% 1.33/1.71 X := T
% 1.33/1.71 Y := line_connecting( X, Y )
% 1.33/1.71 Z := Z
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (118) {G1,W14,D3,L4,V4,M1} R(11,6) { distinct_points( X, Y ),
% 1.33/1.71 ! distinct_points( Z, T ), distinct_points( Y, Z ), !
% 1.33/1.71 apart_point_and_line( X, line_connecting( Z, T ) ) }.
% 1.33/1.71 parent0: (991) {G1,W14,D3,L4,V4,M4} { ! distinct_points( X, Y ),
% 1.33/1.71 distinct_points( Z, X ), distinct_points( T, Z ), ! apart_point_and_line
% 1.33/1.71 ( T, line_connecting( X, Y ) ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := Z
% 1.33/1.71 Y := T
% 1.33/1.71 Z := Y
% 1.33/1.71 T := X
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 1
% 1.33/1.71 1 ==> 2
% 1.33/1.71 2 ==> 0
% 1.33/1.71 3 ==> 3
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 factor: (994) {G1,W11,D3,L3,V2,M3} { distinct_points( X, X ), !
% 1.33/1.71 distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X, Y
% 1.33/1.71 ) ) }.
% 1.33/1.71 parent0[0, 2]: (118) {G1,W14,D3,L4,V4,M1} R(11,6) { distinct_points( X, Y )
% 1.33/1.71 , ! distinct_points( Z, T ), distinct_points( Y, Z ), !
% 1.33/1.71 apart_point_and_line( X, line_connecting( Z, T ) ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := X
% 1.33/1.71 Y := X
% 1.33/1.71 Z := X
% 1.33/1.71 T := Y
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 resolution: (995) {G1,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 1.33/1.71 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.33/1.71 parent0[0]: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 1.33/1.71 parent1[0]: (994) {G1,W11,D3,L3,V2,M3} { distinct_points( X, X ), !
% 1.33/1.71 distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X, Y
% 1.33/1.71 ) ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := X
% 1.33/1.71 end
% 1.33/1.71 substitution1:
% 1.33/1.71 X := X
% 1.33/1.71 Y := Y
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (121) {G2,W8,D3,L2,V2,M1} F(118);r(0) { ! distinct_points( X,
% 1.33/1.71 Y ), ! apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.33/1.71 parent0: (995) {G1,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 1.33/1.71 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := X
% 1.33/1.71 Y := Y
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 0
% 1.33/1.71 1 ==> 1
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 factor: (996) {G1,W11,D3,L3,V2,M3} { distinct_points( X, X ), !
% 1.33/1.71 distinct_points( Y, X ), ! apart_point_and_line( X, line_connecting( Y, X
% 1.33/1.71 ) ) }.
% 1.33/1.71 parent0[0, 2]: (117) {G1,W14,D3,L4,V4,M1} R(11,7) { distinct_points( X, Y )
% 1.33/1.71 , ! distinct_points( Z, T ), distinct_points( Y, T ), !
% 1.33/1.71 apart_point_and_line( X, line_connecting( Z, T ) ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := X
% 1.33/1.71 Y := X
% 1.33/1.71 Z := Y
% 1.33/1.71 T := X
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 resolution: (997) {G1,W8,D3,L2,V2,M2} { ! distinct_points( Y, X ), !
% 1.33/1.71 apart_point_and_line( X, line_connecting( Y, X ) ) }.
% 1.33/1.71 parent0[0]: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 1.33/1.71 parent1[0]: (996) {G1,W11,D3,L3,V2,M3} { distinct_points( X, X ), !
% 1.33/1.71 distinct_points( Y, X ), ! apart_point_and_line( X, line_connecting( Y, X
% 1.33/1.71 ) ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := X
% 1.33/1.71 end
% 1.33/1.71 substitution1:
% 1.33/1.71 X := X
% 1.33/1.71 Y := Y
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (122) {G2,W8,D3,L2,V2,M1} F(117);r(0) { ! distinct_points( Y,
% 1.33/1.71 X ), ! apart_point_and_line( X, line_connecting( Y, X ) ) }.
% 1.33/1.71 parent0: (997) {G1,W8,D3,L2,V2,M2} { ! distinct_points( Y, X ), !
% 1.33/1.71 apart_point_and_line( X, line_connecting( Y, X ) ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := X
% 1.33/1.71 Y := Y
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 0
% 1.33/1.71 1 ==> 1
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 resolution: (998) {G1,W8,D3,L2,V1,M2} { distinct_lines( line_connecting(
% 1.33/1.71 skol1, skol2 ), X ), apart_point_and_line( skol3, X ) }.
% 1.33/1.71 parent0[2]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 1.33/1.71 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 1.33/1.71 parent1[0]: (15) {G0,W5,D3,L1,V0,M1} I { apart_point_and_line( skol3,
% 1.33/1.71 line_connecting( skol1, skol2 ) ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := skol3
% 1.33/1.71 Y := line_connecting( skol1, skol2 )
% 1.33/1.71 Z := X
% 1.33/1.71 end
% 1.33/1.71 substitution1:
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (139) {G1,W8,D3,L2,V1,M1} R(12,15) { distinct_lines(
% 1.33/1.71 line_connecting( skol1, skol2 ), X ), apart_point_and_line( skol3, X )
% 1.33/1.71 }.
% 1.33/1.71 parent0: (998) {G1,W8,D3,L2,V1,M2} { distinct_lines( line_connecting(
% 1.33/1.71 skol1, skol2 ), X ), apart_point_and_line( skol3, X ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := X
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 0
% 1.33/1.71 1 ==> 1
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 resolution: (999) {G2,W10,D3,L2,V1,M2} { ! distinct_points( skol3, X ),
% 1.33/1.71 distinct_lines( line_connecting( skol1, skol2 ), line_connecting( skol3,
% 1.33/1.71 X ) ) }.
% 1.33/1.71 parent0[1]: (121) {G2,W8,D3,L2,V2,M1} F(118);r(0) { ! distinct_points( X, Y
% 1.33/1.71 ), ! apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.33/1.71 parent1[1]: (139) {G1,W8,D3,L2,V1,M1} R(12,15) { distinct_lines(
% 1.33/1.71 line_connecting( skol1, skol2 ), X ), apart_point_and_line( skol3, X )
% 1.33/1.71 }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := skol3
% 1.33/1.71 Y := X
% 1.33/1.71 end
% 1.33/1.71 substitution1:
% 1.33/1.71 X := line_connecting( skol3, X )
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (142) {G3,W10,D3,L2,V1,M1} R(139,121) { ! distinct_points(
% 1.33/1.71 skol3, X ), distinct_lines( line_connecting( skol1, skol2 ),
% 1.33/1.71 line_connecting( skol3, X ) ) }.
% 1.33/1.71 parent0: (999) {G2,W10,D3,L2,V1,M2} { ! distinct_points( skol3, X ),
% 1.33/1.71 distinct_lines( line_connecting( skol1, skol2 ), line_connecting( skol3,
% 1.33/1.71 X ) ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := X
% 1.33/1.71 end
% 1.33/1.71 permutation0:
% 1.33/1.71 0 ==> 0
% 1.33/1.71 1 ==> 1
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 resolution: (1000) {G3,W13,D3,L3,V2,M3} { distinct_lines( line_connecting
% 1.33/1.71 ( skol3, X ), Y ), distinct_lines( Y, line_connecting( skol1, skol2 ) ),
% 1.33/1.71 ! distinct_points( skol3, X ) }.
% 1.33/1.71 parent0[1]: (28) {G2,W9,D2,L3,V3,M3} R(27,4) { distinct_lines( Z, X ), !
% 1.33/1.71 distinct_lines( Y, Z ), distinct_lines( X, Y ) }.
% 1.33/1.71 parent1[1]: (142) {G3,W10,D3,L2,V1,M1} R(139,121) { ! distinct_points(
% 1.33/1.71 skol3, X ), distinct_lines( line_connecting( skol1, skol2 ),
% 1.33/1.71 line_connecting( skol3, X ) ) }.
% 1.33/1.71 substitution0:
% 1.33/1.71 X := Y
% 1.33/1.71 Y := line_connecting( skol1, skol2 )
% 1.33/1.71 Z := line_connecting( skol3, X )
% 1.33/1.71 end
% 1.33/1.71 substitution1:
% 1.33/1.71 X := X
% 1.33/1.71 end
% 1.33/1.71
% 1.33/1.71 subsumption: (325) {G4,W13,D3,L3,V2,M2} R(142,28) { ! distinct_points(
% 1.33/1.71 skol3, X ), distinct_lines( Y, line_connecting( skol1, skol2 ) ),
% 1.33/1.71 distinct_lines( line_connecting( skol3, X ), Y ) }.
% 1.36/1.71 parent0: (1000) {G3,W13,D3,L3,V2,M3} { distinct_lines( line_connecting(
% 1.36/1.71 skol3, X ), Y ), distinct_lines( Y, line_connecting( skol1, skol2 ) ), !
% 1.36/1.71 distinct_points( skol3, X ) }.
% 1.36/1.71 substitution0:
% 1.36/1.71 X := X
% 1.36/1.71 Y := Y
% 1.36/1.71 end
% 1.36/1.71 permutation0:
% 1.36/1.71 0 ==> 2
% 1.36/1.71 1 ==> 1
% 1.36/1.71 2 ==> 0
% 1.36/1.71 end
% 1.36/1.71
% 1.36/1.71 resolution: (1001) {G2,W17,D3,L5,V1,M5} { ! distinct_points( skol1, skol3
% 1.36/1.71 ), ! distinct_points( skol2, skol3 ), ! distinct_lines( X,
% 1.36/1.71 line_connecting( skol1, skol3 ) ), apart_point_and_line( skol2, X ),
% 1.36/1.71 apart_point_and_line( skol3, X ) }.
% 1.36/1.71 parent0[1]: (122) {G2,W8,D3,L2,V2,M1} F(117);r(0) { ! distinct_points( Y, X
% 1.36/1.71 ), ! apart_point_and_line( X, line_connecting( Y, X ) ) }.
% 1.36/1.71 parent1[2]: (100) {G1,W19,D3,L5,V2,M3} R(10,16) { ! distinct_points( skol2
% 1.36/1.71 , X ), ! distinct_lines( Y, line_connecting( skol1, skol3 ) ),
% 1.36/1.71 apart_point_and_line( X, line_connecting( skol1, skol3 ) ),
% 1.36/1.71 apart_point_and_line( skol2, Y ), apart_point_and_line( X, Y ) }.
% 1.36/1.71 substitution0:
% 1.36/1.71 X := skol3
% 1.36/1.71 Y := skol1
% 1.36/1.71 end
% 1.36/1.71 substitution1:
% 1.36/1.71 X := skol3
% 1.36/1.71 Y := X
% 1.36/1.71 end
% 1.36/1.71
% 1.36/1.71 resolution: (1005) {G3,W14,D3,L4,V1,M4} { ! distinct_points( skol1, skol3
% 1.36/1.71 ), ! distinct_lines( X, line_connecting( skol1, skol3 ) ),
% 1.36/1.71 apart_point_and_line( skol2, X ), apart_point_and_line( skol3, X ) }.
% 1.36/1.71 parent0[1]: (1001) {G2,W17,D3,L5,V1,M5} { ! distinct_points( skol1, skol3
% 1.36/1.71 ), ! distinct_points( skol2, skol3 ), ! distinct_lines( X,
% 1.36/1.71 line_connecting( skol1, skol3 ) ), apart_point_and_line( skol2, X ),
% 1.36/1.71 apart_point_and_line( skol3, X ) }.
% 1.36/1.71 parent1[0]: (56) {G2,W3,D2,L1,V0,M1} R(55,20) { distinct_points( skol2,
% 1.36/1.71 skol3 ) }.
% 1.36/1.71 substitution0:
% 1.36/1.71 X := X
% 1.36/1.71 end
% 1.36/1.71 substitution1:
% 1.36/1.71 end
% 1.36/1.71
% 1.36/1.71 subsumption: (590) {G3,W14,D3,L4,V1,M1} R(100,122);r(56) { ! distinct_lines
% 1.36/1.71 ( X, line_connecting( skol1, skol3 ) ), apart_point_and_line( skol2, X )
% 1.36/1.71 , ! distinct_points( skol1, skol3 ), apart_point_and_line( skol3, X ) }.
% 1.36/1.71 parent0: (1005) {G3,W14,D3,L4,V1,M4} { ! distinct_points( skol1, skol3 ),
% 1.36/1.71 ! distinct_lines( X, line_connecting( skol1, skol3 ) ),
% 1.36/1.71 apart_point_and_line( skol2, X ), apart_point_and_line( skol3, X ) }.
% 1.36/1.71 substitution0:
% 1.36/1.71 X := X
% 1.36/1.71 end
% 1.36/1.71 permutation0:
% 1.36/1.71 0 ==> 2
% 1.36/1.71 1 ==> 0
% 1.36/1.71 2 ==> 1
% 1.36/1.71 3 ==> 3
% 1.36/1.71 end
% 1.36/1.71
% 1.36/1.71 resolution: (1007) {G2,W17,D3,L5,V1,M5} { ! distinct_points( skol1, skol3
% 1.36/1.71 ), ! distinct_points( skol1, skol2 ), ! distinct_lines( line_connecting
% 1.36/1.71 ( skol1, skol3 ), X ), apart_point_and_line( skol2, X ),
% 1.36/1.71 apart_point_and_line( skol1, X ) }.
% 1.36/1.71 parent0[1]: (121) {G2,W8,D3,L2,V2,M1} F(118);r(0) { ! distinct_points( X, Y
% 1.36/1.71 ), ! apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.36/1.71 parent1[3]: (101) {G1,W19,D3,L5,V2,M3} R(10,16) { ! distinct_points( X,
% 1.36/1.71 skol2 ), ! distinct_lines( line_connecting( skol1, skol3 ), Y ),
% 1.36/1.71 apart_point_and_line( skol2, Y ), apart_point_and_line( X,
% 1.36/1.71 line_connecting( skol1, skol3 ) ), apart_point_and_line( X, Y ) }.
% 1.36/1.71 substitution0:
% 1.36/1.71 X := skol1
% 1.36/1.71 Y := skol3
% 1.36/1.71 end
% 1.36/1.71 substitution1:
% 1.36/1.71 X := skol1
% 1.36/1.71 Y := X
% 1.36/1.71 end
% 1.36/1.71
% 1.36/1.71 resolution: (1010) {G1,W14,D3,L4,V1,M4} { ! distinct_points( skol1, skol3
% 1.36/1.71 ), ! distinct_lines( line_connecting( skol1, skol3 ), X ),
% 1.36/1.71 apart_point_and_line( skol2, X ), apart_point_and_line( skol1, X ) }.
% 1.36/1.71 parent0[1]: (1007) {G2,W17,D3,L5,V1,M5} { ! distinct_points( skol1, skol3
% 1.36/1.71 ), ! distinct_points( skol1, skol2 ), ! distinct_lines( line_connecting
% 1.36/1.71 ( skol1, skol3 ), X ), apart_point_and_line( skol2, X ),
% 1.36/1.71 apart_point_and_line( skol1, X ) }.
% 1.36/1.71 parent1[0]: (14) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol1, skol2 )
% 1.36/1.71 }.
% 1.36/1.71 substitution0:
% 1.36/1.71 X := X
% 1.36/1.71 end
% 1.36/1.71 substitution1:
% 1.36/1.71 end
% 1.36/1.71
% 1.36/1.71 subsumption: (591) {G3,W14,D3,L4,V1,M1} R(101,121);r(14) { ! distinct_lines
% 1.36/1.71 ( line_connecting( skol1, skol3 ), X ), apart_point_and_line( skol1, X )
% 1.36/1.71 , ! distinct_points( skol1, skol3 ), apart_point_and_line( skol2, X ) }.
% 1.36/1.71 parent0: (1010) {G1,W14,D3,L4,V1,M4} { ! distinct_points( skol1, skol3 ),
% 1.36/1.71 ! distinct_lines( line_connecting( skol1, skol3 ), X ),
% 1.36/1.71 apart_point_and_line( skol2, X ), apart_point_and_line( skol1, X ) }.
% 1.36/1.71 substitution0:
% 1.36/1.71 X := X
% 1.36/1.71 end
% 1.36/1.71 permutation0:
% 1.36/1.71 0 ==> 2
% 1.36/1.71 1 ==> 0
% 1.36/1.71 2 ==> 3
% 1.36/1.71 3 ==> 1
% 1.36/1.71 end
% 1.36/1.71
% 1.36/1.71 resolution: (1011) {G3,W11,D3,L3,V1,M3} { ! distinct_lines(
% 1.36/1.71 line_connecting( skol1, skol3 ), X ), apart_point_and_line( skol1, X ),
% 1.36/1.71 apart_point_and_line( skol2, X ) }.
% 1.36/1.71 parent0[2]: (591) {G3,W14,D3,L4,V1,M1} R(101,121);r(14) { ! distinct_lines
% 1.36/1.71 ( line_connecting( skol1, skol3 ), X ), apart_point_and_line( skol1, X )
% 1.36/1.71 , ! distinct_points( skol1, skol3 ), apart_point_and_line( skol2, X ) }.
% 1.36/1.71 parent1[0]: (49) {G2,W3,D2,L1,V0,M1} R(48,20) { distinct_points( skol1,
% 1.36/1.71 skol3 ) }.
% 1.36/1.71 substitution0:
% 1.36/1.71 X := X
% 1.36/1.71 end
% 1.36/1.71 substitution1:
% 1.36/1.71 end
% 1.36/1.71
% 1.36/1.71 subsumption: (593) {G4,W11,D3,L3,V1,M1} S(591);r(49) { ! distinct_lines(
% 1.36/1.71 line_connecting( skol1, skol3 ), X ), apart_point_and_line( skol1, X ),
% 1.36/1.71 apart_point_and_line( skol2, X ) }.
% 1.36/1.71 parent0: (1011) {G3,W11,D3,L3,V1,M3} { ! distinct_lines( line_connecting(
% 1.36/1.71 skol1, skol3 ), X ), apart_point_and_line( skol1, X ),
% 1.36/1.71 apart_point_and_line( skol2, X ) }.
% 1.36/1.71 substitution0:
% 1.36/1.71 X := X
% 1.36/1.71 end
% 1.36/1.71 permutation0:
% 1.36/1.71 0 ==> 0
% 1.36/1.71 1 ==> 1
% 1.36/1.71 2 ==> 2
% 1.36/1.71 end
% 1.36/1.71
% 1.36/1.71 resolution: (1013) {G3,W15,D3,L3,V1,M3} { ! distinct_points( X, skol2 ), !
% 1.36/1.71 distinct_lines( line_connecting( skol1, skol3 ), line_connecting( X,
% 1.36/1.71 skol2 ) ), apart_point_and_line( skol1, line_connecting( X, skol2 ) ) }.
% 1.36/1.71 parent0[1]: (122) {G2,W8,D3,L2,V2,M1} F(117);r(0) { ! distinct_points( Y, X
% 1.36/1.71 ), ! apart_point_and_line( X, line_connecting( Y, X ) ) }.
% 1.36/1.71 parent1[2]: (593) {G4,W11,D3,L3,V1,M1} S(591);r(49) { ! distinct_lines(
% 1.36/1.71 line_connecting( skol1, skol3 ), X ), apart_point_and_line( skol1, X ),
% 1.36/1.71 apart_point_and_line( skol2, X ) }.
% 1.36/1.71 substitution0:
% 1.36/1.71 X := skol2
% 1.36/1.71 Y := X
% 1.36/1.71 end
% 1.36/1.71 substitution1:
% 1.36/1.71 X := line_connecting( X, skol2 )
% 1.36/1.71 end
% 1.36/1.71
% 1.36/1.71 subsumption: (598) {G5,W15,D3,L3,V1,M1} R(593,122) { ! distinct_lines(
% 1.36/1.71 line_connecting( skol1, skol3 ), line_connecting( X, skol2 ) ), !
% 1.36/1.71 distinct_points( X, skol2 ), apart_point_and_line( skol1, line_connecting
% 1.36/1.71 ( X, skol2 ) ) }.
% 1.36/1.71 parent0: (1013) {G3,W15,D3,L3,V1,M3} { ! distinct_points( X, skol2 ), !
% 1.36/1.71 distinct_lines( line_connecting( skol1, skol3 ), line_connecting( X,
% 1.36/1.71 skol2 ) ), apart_point_and_line( skol1, line_connecting( X, skol2 ) ) }.
% 1.36/1.71 substitution0:
% 1.36/1.71 X := X
% 1.36/1.71 end
% 1.36/1.71 permutation0:
% 1.36/1.71 0 ==> 1
% 1.36/1.71 1 ==> 0
% 1.36/1.71 2 ==> 2
% 1.36/1.71 end
% 1.36/1.71
% 1.36/1.71 resolution: (1014) {G3,W11,D3,L3,V1,M3} { ! distinct_lines( X,
% 1.36/1.71 line_connecting( skol1, skol3 ) ), apart_point_and_line( skol2, X ),
% 1.36/1.71 apart_point_and_line( skol3, X ) }.
% 1.36/1.71 parent0[2]: (590) {G3,W14,D3,L4,V1,M1} R(100,122);r(56) { ! distinct_lines
% 1.36/1.71 ( X, line_connecting( skol1, skol3 ) ), apart_point_and_line( skol2, X )
% 1.36/1.71 , ! distinct_points( skol1, skol3 ), apart_point_and_line( skol3, X ) }.
% 1.36/1.71 parent1[0]: (49) {G2,W3,D2,L1,V0,M1} R(48,20) { distinct_points( skol1,
% 1.36/1.71 skol3 ) }.
% 1.36/1.71 substitution0:
% 1.36/1.71 X := X
% 1.36/1.71 end
% 1.36/1.71 substitution1:
% 1.36/1.71 end
% 1.36/1.71
% 1.36/1.71 subsumption: (614) {G4,W11,D3,L3,V1,M1} S(590);r(49) { ! distinct_lines( X
% 1.36/1.71 , line_connecting( skol1, skol3 ) ), apart_point_and_line( skol2, X ),
% 1.36/1.71 apart_point_and_line( skol3, X ) }.
% 1.36/1.71 parent0: (1014) {G3,W11,D3,L3,V1,M3} { ! distinct_lines( X,
% 1.36/1.71 line_connecting( skol1, skol3 ) ), apart_point_and_line( skol2, X ),
% 1.36/1.71 apart_point_and_line( skol3, X ) }.
% 1.36/1.71 substitution0:
% 1.36/1.71 X := X
% 1.36/1.71 end
% 1.36/1.71 permutation0:
% 1.36/1.71 0 ==> 0
% 1.36/1.71 1 ==> 1
% 1.36/1.71 2 ==> 2
% 1.36/1.71 end
% 1.36/1.71
% 1.36/1.71 resolution: (1016) {G3,W15,D3,L3,V1,M3} { ! distinct_points( skol3, X ), !
% 1.36/1.71 distinct_lines( line_connecting( skol3, X ), line_connecting( skol1,
% 1.36/1.71 skol3 ) ), apart_point_and_line( skol2, line_connecting( skol3, X ) ) }.
% 1.36/1.71 parent0[1]: (121) {G2,W8,D3,L2,V2,M1} F(118);r(0) { ! distinct_points( X, Y
% 1.36/1.71 ), ! apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.36/1.71 parent1[2]: (614) {G4,W11,D3,L3,V1,M1} S(590);r(49) { ! distinct_lines( X,
% 1.36/1.71 line_connecting( skol1, skol3 ) ), apart_point_and_line( skol2, X ),
% 1.36/1.71 apart_point_and_line( skol3, X ) }.
% 1.36/1.71 substitution0:
% 1.36/1.71 X := skol3
% 1.36/1.71 Y := X
% 1.36/1.71 end
% 1.36/1.71 substitution1:
% 1.36/1.71 X := line_connecting( skol3, X )
% 1.36/1.71 end
% 1.36/1.71
% 1.36/1.71 subsumption: (618) {G5,W15,D3,L3,V1,M1} R(614,121) { ! distinct_lines(
% 1.36/1.71 line_connecting( skol3, X ), line_connecting( skol1, skol3 ) ), !
% 1.36/1.71 distinct_points( skol3, X ), apart_point_and_line( skol2, line_connecting
% 1.36/1.71 ( skol3, X ) ) }.
% 1.36/1.71 parent0: (1016) {G3,W15,D3,L3,V1,M3} { ! distinct_points( skol3, X ), !
% 1.36/1.71 distinct_lines( line_connecting( skol3, X ), line_connecting( skol1,
% 1.36/1.71 skol3 ) ), apart_point_and_line( skol2, line_connecting( skol3, X ) ) }.
% 1.36/1.71 substitution0:
% 1.36/1.71 X := X
% 1.36/1.71 end
% 1.36/1.71 permutation0:
% 1.36/1.71 0 ==> 1
% 1.36/1.71 1 ==> 0
% 1.36/1.71 2 ==> 2
% 1.36/1.71 end
% 1.36/1.71
% 1.36/1.71 resolution: (1017) {G3,W13,D3,L3,V0,M3} { ! distinct_points( skol3, skol2
% 1.36/1.71 ), ! distinct_lines( line_connecting( skol3, skol2 ), line_connecting(
% 1.36/1.71 skol1, skol3 ) ), ! distinct_points( skol3, skol2 ) }.
% 1.36/1.71 parent0[1]: (122) {G2,W8,D3,L2,V2,M1} F(117);r(0) { ! distinct_points( Y, X
% 1.36/1.71 ), ! apart_point_and_line( X, line_connecting( Y, X ) ) }.
% 1.36/1.71 parent1[2]: (618) {G5,W15,D3,L3,V1,M1} R(614,121) { ! distinct_lines(
% 1.36/1.71 line_connecting( skol3, X ), line_connecting( skol1, skol3 ) ), !
% 1.36/1.71 distinct_points( skol3, X ), apart_point_and_line( skol2, line_connecting
% 1.36/1.71 ( skol3, X ) ) }.
% 1.36/1.71 substitution0:
% 1.36/1.71 X := skol2
% 1.36/1.71 Y := skol3
% 1.36/1.71 end
% 1.36/1.71 substitution1:
% 1.36/1.71 X := skol2
% 1.36/1.71 end
% 1.36/1.71
% 1.36/1.71 factor: (1018) {G3,W10,D3,L2,V0,M2} { ! distinct_points( skol3, skol2 ), !
% 1.36/1.71 distinct_lines( line_connecting( skol3, skol2 ), line_connecting( skol1
% 1.36/1.71 , skol3 ) ) }.
% 1.36/1.71 parent0[0, 2]: (1017) {G3,W13,D3,L3,V0,M3} { ! distinct_points( skol3,
% 1.36/1.71 skol2 ), ! distinct_lines( line_connecting( skol3, skol2 ),
% 1.36/1.71 line_connecting( skol1, skol3 ) ), ! distinct_points( skol3, skol2 ) }.
% 1.36/1.71 substitution0:
% 1.36/1.71 end
% 1.36/1.71
% 1.36/1.71 resolution: (1020) {G2,W7,D3,L1,V0,M1} { ! distinct_lines( line_connecting
% 1.36/1.71 ( skol3, skol2 ), line_connecting( skol1, skol3 ) ) }.
% 1.36/1.71 parent0[0]: (1018) {G3,W10,D3,L2,V0,M2} { ! distinct_points( skol3, skol2
% 1.36/1.71 ), ! distinct_lines( line_connecting( skol3, skol2 ), line_connecting(
% 1.36/1.71 skol1, skol3 ) ) }.
% 1.36/1.71 parent1[0]: (55) {G1,W3,D2,L1,V0,M1} R(7,15);r(14) { distinct_points( skol3
% 1.36/1.71 , skol2 ) }.
% 1.36/1.71 substitution0:
% 1.36/1.71 end
% 1.36/1.71 substitution1:
% 1.36/1.71 end
% 1.36/1.71
% 1.36/1.71 subsumption: (622) {G6,W7,D3,L1,V0,M1} R(618,122);f;r(55) { !
% 1.36/1.71 distinct_lines( line_connecting( skol3, skol2 ), line_connecting( skol1,
% 1.36/1.71 skol3 ) ) }.
% 1.36/1.71 parent0: (1020) {G2,W7,D3,L1,V0,M1} { ! distinct_lines( line_connecting(
% 1.36/1.71 skol3, skol2 ), line_connecting( skol1, skol3 ) ) }.
% 1.36/1.71 substitution0:
% 1.36/1.71 end
% 1.36/1.71 permutation0:
% 1.36/1.71 0 ==> 0
% 1.36/1.71 end
% 1.36/1.71
% 1.36/1.71 resolution: (1021) {G5,W10,D3,L2,V0,M2} { ! distinct_points( skol3, skol2
% 1.36/1.71 ), distinct_lines( line_connecting( skol1, skol3 ), line_connecting(
% 1.36/1.71 skol1, skol2 ) ) }.
% 1.36/1.71 parent0[0]: (622) {G6,W7,D3,L1,V0,M1} R(618,122);f;r(55) { ! distinct_lines
% 1.36/1.71 ( line_connecting( skol3, skol2 ), line_connecting( skol1, skol3 ) ) }.
% 1.36/1.71 parent1[2]: (325) {G4,W13,D3,L3,V2,M2} R(142,28) { ! distinct_points( skol3
% 1.36/1.71 , X ), distinct_lines( Y, line_connecting( skol1, skol2 ) ),
% 1.36/1.71 distinct_lines( line_connecting( skol3, X ), Y ) }.
% 1.36/1.71 substitution0:
% 1.36/1.71 end
% 1.36/1.71 substitution1:
% 1.36/1.71 X := skol2
% 1.36/1.71 Y := line_connecting( skol1, skol3 )
% 1.36/1.71 end
% 1.36/1.71
% 1.36/1.71 resolution: (1022) {G2,W7,D3,L1,V0,M1} { distinct_lines( line_connecting(
% 1.36/1.71 skol1, skol3 ), line_connecting( skol1, skol2 ) ) }.
% 1.36/1.71 parent0[0]: (1021) {G5,W10,D3,L2,V0,M2} { ! distinct_points( skol3, skol2
% 1.36/1.71 ), distinct_lines( line_connecting( skol1, skol3 ), line_connecting(
% 1.36/1.71 skol1, skol2 ) ) }.
% 1.36/1.71 parent1[0]: (55) {G1,W3,D2,L1,V0,M1} R(7,15);r(14) { distinct_points( skol3
% 1.36/1.71 , skol2 ) }.
% 1.36/1.71 substitution0:
% 1.36/1.71 end
% 1.36/1.71 substitution1:
% 1.36/1.71 end
% 1.36/1.71
% 1.36/1.71 subsumption: (625) {G7,W7,D3,L1,V0,M1} R(622,325);r(55) { distinct_lines(
% 1.36/1.71 line_connecting( skol1, skol3 ), line_connecting( skol1, skol2 ) ) }.
% 1.36/1.71 parent0: (1022) {G2,W7,D3,L1,V0,M1} { distinct_lines( line_connecting(
% 1.36/1.71 skol1, skol3 ), line_connecting( skol1, skol2 ) ) }.
% 1.36/1.71 substitution0:
% 1.36/1.71 end
% 1.36/1.71 permutation0:
% 1.36/1.71 0 ==> 0
% 1.36/1.71 end
% 1.36/1.71
% 1.36/1.71 resolution: (1023) {G3,W13,D3,L3,V0,M3} { ! distinct_points( skol1, skol2
% 1.36/1.71 ), ! distinct_lines( line_connecting( skol1, skol3 ), line_connecting(
% 1.36/1.71 skol1, skol2 ) ), ! distinct_points( skol1, skol2 ) }.
% 1.36/1.71 parent0[1]: (121) {G2,W8,D3,L2,V2,M1} F(118);r(0) { ! distinct_points( X, Y
% 1.36/1.71 ), ! apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.36/1.71 parent1[2]: (598) {G5,W15,D3,L3,V1,M1} R(593,122) { ! distinct_lines(
% 1.36/1.71 line_connecting( skol1, skol3 ), line_connecting( X, skol2 ) ), !
% 1.36/1.71 distinct_points( X, skol2 ), apart_point_and_line( skol1, line_connecting
% 1.36/1.71 ( X, skol2 ) ) }.
% 1.36/1.71 substitution0:
% 1.36/1.71 X := skol1
% 1.36/1.71 Y := skol2
% 1.36/1.71 end
% 1.36/1.71 substitution1:
% 1.36/1.71 X := skol1
% 1.36/1.71 end
% 1.36/1.71
% 1.36/1.71 resolution: (1025) {G4,W6,D2,L2,V0,M2} { ! distinct_points( skol1, skol2 )
% 1.36/1.71 , ! distinct_points( skol1, skol2 ) }.
% 1.36/1.71 parent0[1]: (1023) {G3,W13,D3,L3,V0,M3} { ! distinct_points( skol1, skol2
% 1.36/1.71 ), ! distinct_lines( line_connecting( skol1, skol3 ), line_connecting(
% 1.36/1.71 skol1, skol2 ) ), ! distinct_points( skol1, skol2 ) }.
% 1.36/1.71 parent1[0]: (625) {G7,W7,D3,L1,V0,M1} R(622,325);r(55) { distinct_lines(
% 1.36/1.71 line_connecting( skol1, skol3 ), line_connecting( skol1, skol2 ) ) }.
% 1.36/1.71 substitution0:
% 1.36/1.71 end
% 1.36/1.71 substitution1:
% 1.36/1.71 end
% 1.36/1.71
% 1.36/1.71 factor: (1026) {G4,W3,D2,L1,V0,M1} { ! distinct_points( skol1, skol2 ) }.
% 1.36/1.71 parent0[0, 1]: (1025) {G4,W6,D2,L2,V0,M2} { ! distinct_points( skol1,
% 1.36/1.71 skol2 ), ! distinct_points( skol1, skol2 ) }.
% 1.36/1.71 substitution0:
% 1.36/1.71 end
% 1.36/1.71
% 1.36/1.71 subsumption: (870) {G8,W3,D2,L1,V0,M1} R(598,121);f;r(625) { !
% 1.36/1.71 distinct_points( skol1, skol2 ) }.
% 1.36/1.71 parent0: (1026) {G4,W3,D2,L1,V0,M1} { ! distinct_points( skol1, skol2 )
% 1.36/1.71 }.
% 1.36/1.71 substitution0:
% 1.36/1.71 end
% 1.36/1.71 permutation0:
% 1.36/1.71 0 ==> 0
% 1.36/1.71 end
% 1.36/1.71
% 1.36/1.71 resolution: (1027) {G1,W0,D0,L0,V0,M0} { }.
% 1.36/1.71 parent0[0]: (870) {G8,W3,D2,L1,V0,M1} R(598,121);f;r(625) { !
% 1.36/1.71 distinct_points( skol1, skol2 ) }.
% 1.36/1.71 parent1[0]: (14) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol1, skol2 )
% 1.36/1.71 }.
% 1.36/1.71 substitution0:
% 1.36/1.71 end
% 1.36/1.71 substitution1:
% 1.36/1.71 end
% 1.36/1.71
% 1.36/1.71 subsumption: (873) {G9,W0,D0,L0,V0,M0} S(870);r(14) { }.
% 1.36/1.71 parent0: (1027) {G1,W0,D0,L0,V0,M0} { }.
% 1.36/1.71 substitution0:
% 1.36/1.71 end
% 1.36/1.71 permutation0:
% 1.36/1.71 end
% 1.36/1.71
% 1.36/1.71 Proof check complete!
% 1.36/1.71
% 1.36/1.71 Memory use:
% 1.36/1.71
% 1.36/1.71 space for terms: 12351
% 1.36/1.71 space for clauses: 33793
% 1.36/1.71
% 1.36/1.71
% 1.36/1.71 clauses generated: 76724
% 1.36/1.71 clauses kept: 874
% 1.36/1.71 clauses selected: 642
% 1.36/1.71 clauses deleted: 5
% 1.36/1.71 clauses inuse deleted: 0
% 1.36/1.71
% 1.36/1.71 subsentry: 97416
% 1.36/1.71 literals s-matched: 73310
% 1.36/1.71 literals matched: 73280
% 1.36/1.71 full subsumption: 62669
% 1.36/1.71
% 1.36/1.71 checksum: 2141605193
% 1.36/1.71
% 1.36/1.71
% 1.36/1.71 Bliksem ended
%------------------------------------------------------------------------------