%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO186+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n014.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 02:52:26 EDT 2022
% Result : Theorem 5.95s 6.32s
% Output : Refutation 5.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : GEO186+3 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.14 % Command : bliksem %s
% 0.14/0.36 % Computer : n014.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % DateTime : Fri Jun 17 15:35:49 EDT 2022
% 0.14/0.36 % CPUTime :
% 3.51/3.91 *** allocated 10000 integers for termspace/termends
% 3.51/3.91 *** allocated 10000 integers for clauses
% 3.51/3.91 *** allocated 10000 integers for justifications
% 3.51/3.91 Bliksem 1.12
% 3.51/3.91
% 3.51/3.91
% 3.51/3.91 Automatic Strategy Selection
% 3.51/3.91
% 3.51/3.91
% 3.51/3.91 Clauses:
% 3.51/3.91
% 3.51/3.91 { ! distinct_points( X, X ) }.
% 3.51/3.91 { ! distinct_lines( X, X ) }.
% 3.51/3.91 { ! convergent_lines( X, X ) }.
% 3.51/3.91 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 3.51/3.91 ) }.
% 3.51/3.91 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 3.51/3.91 }.
% 3.51/3.91 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 3.51/3.91 , Z ) }.
% 3.51/3.91 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 3.51/3.91 , Y ) ) }.
% 3.51/3.91 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 3.51/3.91 , Y ) ) }.
% 3.51/3.91 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 3.51/3.91 , Y ), X ) }.
% 3.51/3.91 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 3.51/3.91 , Y ), Y ) }.
% 3.51/3.91 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 3.51/3.91 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 3.51/3.91 apart_point_and_line( Y, T ) }.
% 3.51/3.91 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 3.51/3.91 apart_point_and_line( Z, Y ) }.
% 3.51/3.91 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 3.51/3.91 apart_point_and_line( X, Z ) }.
% 3.51/3.91 { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X,
% 3.51/3.91 Z ) }.
% 3.51/3.91 { ! distinct_lines( X, Y ), convergent_lines( X, Y ) }.
% 3.51/3.91 { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 3.51/3.91 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 3.51/3.91 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 3.51/3.91 apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 3.51/3.91 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 3.51/3.91 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 3.51/3.91 , convergent_lines( Y, Z ) }.
% 3.51/3.91 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 3.51/3.91 , unorthogonal_lines( Y, Z ) }.
% 3.51/3.91 { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 3.51/3.91 { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 3.51/3.91 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 3.51/3.91 }.
% 3.51/3.91 { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 3.51/3.91 { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 3.51/3.91 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 3.51/3.91 apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ),
% 3.51/3.91 unorthogonal_lines( Y, T ) }.
% 3.51/3.91 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 3.51/3.91 { alpha2( X, Z ), convergent_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 3.51/3.91 unorthogonal_lines( X, Y ) }.
% 3.51/3.91 { alpha2( X, Z ), unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 3.51/3.91 unorthogonal_lines( X, Y ) }.
% 3.51/3.91 { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 3.51/3.91 { ! alpha2( X, Y ), unorthogonal_lines( Y, X ) }.
% 3.51/3.91 { ! convergent_lines( Y, X ), ! unorthogonal_lines( Y, X ), alpha2( X, Y )
% 3.51/3.91 }.
% 3.51/3.91 { unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ), !
% 3.51/3.91 convergent_lines( X, Y ) }.
% 3.51/3.91 { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line(
% 3.51/3.91 line_connecting( X, Y ) ) }.
% 3.51/3.91 { ! line( X ), ! line( Y ), ! convergent_lines( X, Y ), point(
% 3.51/3.91 intersection_point( X, Y ) ) }.
% 3.51/3.91 { ! line( X ), ! point( Y ), line( parallel_through_point( X, Y ) ) }.
% 3.51/3.91 { ! line( X ), ! point( Y ), line( orthogonal_through_point( X, Y ) ) }.
% 3.51/3.91 { ! equal_points( X, Y ), ! distinct_points( X, Y ) }.
% 3.51/3.91 { distinct_points( X, Y ), equal_points( X, Y ) }.
% 3.51/3.91 { ! equal_lines( X, Y ), ! distinct_lines( X, Y ) }.
% 3.51/3.91 { distinct_lines( X, Y ), equal_lines( X, Y ) }.
% 3.51/3.91 { ! parallel_lines( X, Y ), ! convergent_lines( X, Y ) }.
% 3.51/3.91 { convergent_lines( X, Y ), parallel_lines( X, Y ) }.
% 3.51/3.91 { ! incident_point_and_line( X, Y ), ! apart_point_and_line( X, Y ) }.
% 3.51/3.91 { apart_point_and_line( X, Y ), incident_point_and_line( X, Y ) }.
% 3.51/3.91 { ! orthogonal_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 3.51/3.91 { unorthogonal_lines( X, Y ), orthogonal_lines( X, Y ) }.
% 3.51/3.91 { distinct_points( skol1, skol4 ) }.
% 3.51/3.91 { convergent_lines( skol2, skol3 ) }.
% 3.51/3.91 { incident_point_and_line( skol1, skol2 ) }.
% 3.51/3.91 { incident_point_and_line( skol1, skol3 ) }.
% 3.51/3.91 { ! equal_points( skol1, intersection_point( skol2, skol3 ) ) }.
% 3.51/3.91
% 3.51/3.91 percentage equality = 0.000000, percentage horn = 0.627451
% 5.95/6.32 This a non-horn, non-equality problem
% 5.95/6.32
% 5.95/6.32
% 5.95/6.32 Options Used:
% 5.95/6.32
% 5.95/6.32 useres = 1
% 5.95/6.32 useparamod = 0
% 5.95/6.32 useeqrefl = 0
% 5.95/6.32 useeqfact = 0
% 5.95/6.32 usefactor = 1
% 5.95/6.32 usesimpsplitting = 0
% 5.95/6.32 usesimpdemod = 0
% 5.95/6.32 usesimpres = 3
% 5.95/6.32
% 5.95/6.32 resimpinuse = 1000
% 5.95/6.32 resimpclauses = 20000
% 5.95/6.32 substype = standard
% 5.95/6.32 backwardsubs = 1
% 5.95/6.32 selectoldest = 5
% 5.95/6.32
% 5.95/6.32 litorderings [0] = split
% 5.95/6.32 litorderings [1] = liftord
% 5.95/6.32
% 5.95/6.32 termordering = none
% 5.95/6.32
% 5.95/6.32 litapriori = 1
% 5.95/6.32 termapriori = 0
% 5.95/6.32 litaposteriori = 0
% 5.95/6.32 termaposteriori = 0
% 5.95/6.32 demodaposteriori = 0
% 5.95/6.32 ordereqreflfact = 0
% 5.95/6.32
% 5.95/6.32 litselect = none
% 5.95/6.32
% 5.95/6.32 maxweight = 15
% 5.95/6.32 maxdepth = 30000
% 5.95/6.32 maxlength = 115
% 5.95/6.32 maxnrvars = 195
% 5.95/6.32 excuselevel = 1
% 5.95/6.32 increasemaxweight = 1
% 5.95/6.32
% 5.95/6.32 maxselected = 10000000
% 5.95/6.32 maxnrclauses = 10000000
% 5.95/6.32
% 5.95/6.32 showgenerated = 0
% 5.95/6.32 showkept = 0
% 5.95/6.32 showselected = 0
% 5.95/6.32 showdeleted = 0
% 5.95/6.32 showresimp = 1
% 5.95/6.32 showstatus = 2000
% 5.95/6.32
% 5.95/6.32 prologoutput = 0
% 5.95/6.32 nrgoals = 5000000
% 5.95/6.32 totalproof = 1
% 5.95/6.32
% 5.95/6.32 Symbols occurring in the translation:
% 5.95/6.32
% 5.95/6.32 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 5.95/6.32 . [1, 2] (w:1, o:27, a:1, s:1, b:0),
% 5.95/6.32 ! [4, 1] (w:0, o:20, a:1, s:1, b:0),
% 5.95/6.32 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 5.95/6.32 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 5.95/6.32 distinct_points [36, 2] (w:1, o:52, a:1, s:1, b:0),
% 5.95/6.32 distinct_lines [37, 2] (w:1, o:53, a:1, s:1, b:0),
% 5.95/6.32 convergent_lines [38, 2] (w:1, o:51, a:1, s:1, b:0),
% 5.95/6.32 line_connecting [41, 2] (w:1, o:54, a:1, s:1, b:0),
% 5.95/6.32 apart_point_and_line [42, 2] (w:1, o:55, a:1, s:1, b:0),
% 5.95/6.32 intersection_point [43, 2] (w:1, o:56, a:1, s:1, b:0),
% 5.95/6.32 parallel_through_point [46, 2] (w:1, o:59, a:1, s:1, b:0),
% 5.95/6.32 unorthogonal_lines [49, 2] (w:1, o:60, a:1, s:1, b:0),
% 5.95/6.32 orthogonal_through_point [52, 2] (w:1, o:57, a:1, s:1, b:0),
% 5.95/6.32 point [54, 1] (w:1, o:25, a:1, s:1, b:0),
% 5.95/6.32 line [55, 1] (w:1, o:26, a:1, s:1, b:0),
% 5.95/6.32 equal_points [56, 2] (w:1, o:61, a:1, s:1, b:0),
% 5.95/6.32 equal_lines [57, 2] (w:1, o:62, a:1, s:1, b:0),
% 5.95/6.32 parallel_lines [58, 2] (w:1, o:63, a:1, s:1, b:0),
% 5.95/6.32 incident_point_and_line [59, 2] (w:1, o:64, a:1, s:1, b:0),
% 5.95/6.32 orthogonal_lines [60, 2] (w:1, o:58, a:1, s:1, b:0),
% 5.95/6.32 alpha1 [61, 2] (w:1, o:65, a:1, s:1, b:0),
% 5.95/6.32 alpha2 [62, 2] (w:1, o:66, a:1, s:1, b:0),
% 5.95/6.32 skol1 [63, 0] (w:1, o:16, a:1, s:1, b:0),
% 5.95/6.32 skol2 [64, 0] (w:1, o:17, a:1, s:1, b:0),
% 5.95/6.32 skol3 [65, 0] (w:1, o:18, a:1, s:1, b:0),
% 5.95/6.32 skol4 [66, 0] (w:1, o:19, a:1, s:1, b:0).
% 5.95/6.32
% 5.95/6.32
% 5.95/6.32 Starting Search:
% 5.95/6.32
% 5.95/6.32 *** allocated 15000 integers for clauses
% 5.95/6.32 *** allocated 22500 integers for clauses
% 5.95/6.32 *** allocated 33750 integers for clauses
% 5.95/6.32 *** allocated 15000 integers for termspace/termends
% 5.95/6.32 *** allocated 50625 integers for clauses
% 5.95/6.32 Resimplifying inuse:
% 5.95/6.32 Done
% 5.95/6.32
% 5.95/6.32 *** allocated 22500 integers for termspace/termends
% 5.95/6.32 *** allocated 75937 integers for clauses
% 5.95/6.32 *** allocated 33750 integers for termspace/termends
% 5.95/6.32 *** allocated 113905 integers for clauses
% 5.95/6.32
% 5.95/6.32 Intermediate Status:
% 5.95/6.32 Generated: 14788
% 5.95/6.32 Kept: 2002
% 5.95/6.32 Inuse: 333
% 5.95/6.32 Deleted: 2
% 5.95/6.32 Deletedinuse: 1
% 5.95/6.32
% 5.95/6.32 Resimplifying inuse:
% 5.95/6.32 Done
% 5.95/6.32
% 5.95/6.32 *** allocated 50625 integers for termspace/termends
% 5.95/6.32 *** allocated 170857 integers for clauses
% 5.95/6.32 Resimplifying inuse:
% 5.95/6.32 Done
% 5.95/6.32
% 5.95/6.32 *** allocated 75937 integers for termspace/termends
% 5.95/6.32
% 5.95/6.32 Intermediate Status:
% 5.95/6.32 Generated: 36687
% 5.95/6.32 Kept: 4047
% 5.95/6.32 Inuse: 484
% 5.95/6.32 Deleted: 4
% 5.95/6.32 Deletedinuse: 1
% 5.95/6.32
% 5.95/6.32 Resimplifying inuse:
% 5.95/6.32 Done
% 5.95/6.32
% 5.95/6.32 *** allocated 256285 integers for clauses
% 5.95/6.32 Resimplifying inuse:
% 5.95/6.32 Done
% 5.95/6.32
% 5.95/6.32 *** allocated 113905 integers for termspace/termends
% 5.95/6.32
% 5.95/6.32 Intermediate Status:
% 5.95/6.32 Generated: 45897
% 5.95/6.32 Kept: 6068
% 5.95/6.32 Inuse: 558
% 5.95/6.32 Deleted: 6
% 5.95/6.32 Deletedinuse: 2
% 5.95/6.32
% 5.95/6.32 Resimplifying inuse:
% 5.95/6.32 Done
% 5.95/6.32
% 5.95/6.32 *** allocated 384427 integers for clauses
% 5.95/6.32 Resimplifying inuse:
% 5.95/6.32 Done
% 5.95/6.32
% 5.95/6.32 *** allocated 170857 integers for termspace/termends
% 5.95/6.32
% 5.95/6.32 Intermediate Status:
% 5.95/6.32 Generated: 74630
% 5.95/6.32 Kept: 8078
% 5.95/6.32 Inuse: 760
% 5.95/6.32 Deleted: 6
% 5.95/6.32 Deletedinuse: 2
% 5.95/6.32
% 5.95/6.32 Resimplifying inuse:
% 5.95/6.32 Done
% 5.95/6.32
% 5.95/6.32 *** allocated 576640 integers for clauses
% 5.95/6.32 Resimplifying inuse:
% 5.95/6.32 Done
% 5.95/6.32
% 5.95/6.32
% 5.95/6.32 Intermediate Status:
% 5.95/6.32 Generated: 355211
% 5.95/6.32 Kept: 10081
% 5.95/6.32 Inuse: 1541
% 5.95/6.32 Deleted: 21
% 5.95/6.32 Deletedinuse: 2
% 5.95/6.32
% 5.95/6.32 Resimplifying inuse:
% 5.95/6.32 Done
% 5.95/6.32
% 5.95/6.32
% 5.95/6.32 Bliksems!, er is een bewijs:
% 5.95/6.32 % SZS status Theorem
% 5.95/6.32 % SZS output start Refutation
% 5.95/6.32
% 5.95/6.32 (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 5.95/6.32 (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 5.95/6.32 (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 5.95/6.32 (3) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ), distinct_points( Y, Z
% 5.95/6.32 ), ! distinct_points( X, Y ) }.
% 5.95/6.32 (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 5.95/6.32 , ! distinct_lines( X, Y ) }.
% 5.95/6.32 (8) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 5.95/6.32 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 5.95/6.32 (9) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 5.95/6.32 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 5.95/6.32 (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! distinct_lines(
% 5.95/6.32 Z, T ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 5.95/6.32 apart_point_and_line( Y, T ), apart_point_and_line( X, Z ) }.
% 5.95/6.32 (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ), convergent_lines(
% 5.95/6.32 X, Z ), distinct_lines( Y, Z ) }.
% 5.95/6.32 (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! distinct_lines( X
% 5.95/6.32 , Y ) }.
% 5.95/6.32 (37) {G0,W6,D2,L2,V2,M1} I { distinct_points( X, Y ), equal_points( X, Y )
% 5.95/6.32 }.
% 5.95/6.32 (42) {G0,W6,D2,L2,V2,M1} I { ! apart_point_and_line( X, Y ), !
% 5.95/6.32 incident_point_and_line( X, Y ) }.
% 5.95/6.32 (47) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol2, skol3 ) }.
% 5.95/6.32 (48) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol1, skol2 ) }.
% 5.95/6.32 (49) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol1, skol3 ) }.
% 5.95/6.32 (50) {G0,W5,D3,L1,V0,M1} I { ! equal_points( skol1, intersection_point(
% 5.95/6.32 skol2, skol3 ) ) }.
% 5.95/6.32 (53) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ),
% 5.95/6.32 distinct_points( X, Y ) }.
% 5.95/6.32 (57) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 5.95/6.32 ( X, Y ) }.
% 5.95/6.32 (58) {G2,W9,D2,L3,V3,M3} R(57,4) { distinct_lines( Z, X ), ! distinct_lines
% 5.95/6.32 ( Y, Z ), distinct_lines( X, Y ) }.
% 5.95/6.32 (59) {G2,W9,D2,L3,V3,M3} R(57,4) { distinct_lines( Z, X ), ! distinct_lines
% 5.95/6.32 ( Z, Y ), distinct_lines( X, Y ) }.
% 5.95/6.32 (76) {G1,W3,D2,L1,V0,M1} R(42,48) { ! apart_point_and_line( skol1, skol2 )
% 5.95/6.32 }.
% 5.95/6.32 (77) {G1,W3,D2,L1,V0,M1} R(42,49) { ! apart_point_and_line( skol1, skol3 )
% 5.95/6.32 }.
% 5.95/6.32 (78) {G1,W5,D3,L1,V0,M1} R(37,50) { distinct_points( skol1,
% 5.95/6.32 intersection_point( skol2, skol3 ) ) }.
% 5.95/6.32 (79) {G2,W5,D3,L1,V0,M1} R(78,53) { distinct_points( intersection_point(
% 5.95/6.32 skol2, skol3 ), skol1 ) }.
% 5.95/6.32 (81) {G1,W22,D3,L6,V4,M3} R(10,9) { ! distinct_points( intersection_point(
% 5.95/6.32 X, Y ), Z ), ! distinct_lines( T, Y ), ! convergent_lines( X, Y ),
% 5.95/6.32 apart_point_and_line( intersection_point( X, Y ), T ),
% 5.95/6.32 apart_point_and_line( Z, T ), apart_point_and_line( Z, Y ) }.
% 5.95/6.32 (146) {G2,W6,D2,L2,V2,M1} R(14,57) { convergent_lines( X, Y ), !
% 5.95/6.32 distinct_lines( Y, X ) }.
% 5.95/6.32 (511) {G3,W9,D2,L3,V3,M2} R(58,146) { convergent_lines( Z, Y ), !
% 5.95/6.32 distinct_lines( X, Y ), distinct_lines( Z, X ) }.
% 5.95/6.32 (529) {G3,W9,D2,L3,V3,M2} R(59,146) { convergent_lines( Z, X ), !
% 5.95/6.32 distinct_lines( X, Y ), distinct_lines( Z, Y ) }.
% 5.95/6.32 (702) {G4,W12,D2,L4,V4,M1} R(511,13) { convergent_lines( X, Y ), !
% 5.95/6.32 convergent_lines( T, Z ), convergent_lines( T, Y ), distinct_lines( X, Z
% 5.95/6.32 ) }.
% 5.95/6.32 (703) {G5,W9,D2,L3,V3,M1} F(702) { convergent_lines( X, Y ), !
% 5.95/6.32 convergent_lines( X, Z ), distinct_lines( X, Z ) }.
% 5.95/6.32 (731) {G6,W12,D2,L4,V4,M1} R(703,529) { convergent_lines( X, Y ), !
% 5.95/6.32 convergent_lines( X, Z ), convergent_lines( T, X ), distinct_lines( T, Z
% 5.95/6.32 ) }.
% 5.95/6.32 (738) {G7,W6,D2,L2,V2,M1} F(731);r(2) { ! convergent_lines( X, Y ),
% 5.95/6.32 distinct_lines( X, Y ) }.
% 5.95/6.32 (917) {G8,W14,D3,L4,V3,M2} R(81,8);f;r(738) { ! convergent_lines( X, Y ), !
% 5.95/6.32 distinct_points( intersection_point( X, Y ), Z ), apart_point_and_line(
% 5.95/6.32 Z, Y ), apart_point_and_line( Z, X ) }.
% 5.95/6.32 (10215) {G9,W11,D3,L3,V1,M1} R(917,77) { ! convergent_lines( X, skol3 ), !
% 5.95/6.32 distinct_points( intersection_point( X, skol3 ), skol1 ),
% 5.95/6.32 apart_point_and_line( skol1, X ) }.
% 5.95/6.32 (10251) {G10,W5,D3,L1,V0,M1} R(10215,76);r(47) { ! distinct_points(
% 5.95/6.32 intersection_point( skol2, skol3 ), skol1 ) }.
% 5.95/6.32 (10256) {G11,W0,D0,L0,V0,M0} S(10251);r(79) { }.
% 5.95/6.32
% 5.95/6.32
% 5.95/6.32 % SZS output end Refutation
% 5.95/6.32 found a proof!
% 5.95/6.32
% 5.95/6.32
% 5.95/6.32 Unprocessed initial clauses:
% 5.95/6.32
% 5.95/6.32 (10258) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 5.95/6.32 (10259) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 5.95/6.32 (10260) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 5.95/6.32 (10261) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points(
% 5.95/6.32 X, Z ), distinct_points( Y, Z ) }.
% 5.95/6.32 (10262) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X
% 5.95/6.32 , Z ), distinct_lines( Y, Z ) }.
% 5.95/6.32 (10263) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines
% 5.95/6.32 ( X, Z ), convergent_lines( Y, Z ) }.
% 5.95/6.32 (10264) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 5.95/6.32 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 5.95/6.32 (10265) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 5.95/6.32 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 5.95/6.32 (10266) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 5.95/6.32 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 5.95/6.32 (10267) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 5.95/6.32 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 5.95/6.32 (10268) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines
% 5.95/6.32 ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 5.95/6.32 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 5.95/6.32 (10269) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 5.95/6.32 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 5.95/6.32 (10270) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 5.95/6.32 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 5.95/6.32 (10271) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), distinct_lines(
% 5.95/6.32 Y, Z ), convergent_lines( X, Z ) }.
% 5.95/6.32 (10272) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ), convergent_lines(
% 5.95/6.32 X, Y ) }.
% 5.95/6.32 (10273) {G0,W5,D3,L1,V2,M1} { ! convergent_lines( parallel_through_point(
% 5.95/6.32 Y, X ), Y ) }.
% 5.95/6.32 (10274) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 5.95/6.32 parallel_through_point( Y, X ) ) }.
% 5.95/6.32 (10275) {G0,W12,D2,L4,V3,M4} { ! distinct_lines( X, Y ),
% 5.95/6.32 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 5.95/6.32 convergent_lines( X, Y ) }.
% 5.95/6.32 (10276) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines
% 5.95/6.32 ( X, Y ) }.
% 5.95/6.32 (10277) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 5.95/6.32 unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 5.95/6.32 (10278) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 5.95/6.32 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 5.95/6.32 }.
% 5.95/6.32 (10279) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines( X, Y )
% 5.95/6.32 }.
% 5.95/6.32 (10280) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 5.95/6.32 }.
% 5.95/6.32 (10281) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( X, Y ), !
% 5.95/6.32 unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 5.95/6.32 (10282) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines(
% 5.95/6.32 orthogonal_through_point( Y, X ), Y ) }.
% 5.95/6.32 (10283) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 5.95/6.32 orthogonal_through_point( Y, X ) ) }.
% 5.95/6.32 (10284) {G0,W15,D2,L5,V4,M5} { ! distinct_lines( X, Y ),
% 5.95/6.32 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 5.95/6.32 unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 5.95/6.32 (10285) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines
% 5.95/6.32 ( X, Y ) }.
% 5.95/6.32 (10286) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), convergent_lines( Z, Y ), !
% 5.95/6.32 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 5.95/6.32 (10287) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), unorthogonal_lines( Z, Y )
% 5.95/6.32 , ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 5.95/6.32 (10288) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), convergent_lines( Y, X )
% 5.95/6.32 }.
% 5.95/6.32 (10289) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), unorthogonal_lines( Y, X )
% 5.95/6.32 }.
% 5.95/6.32 (10290) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( Y, X ), !
% 5.95/6.32 unorthogonal_lines( Y, X ), alpha2( X, Y ) }.
% 5.95/6.32 (10291) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ),
% 5.95/6.32 unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 5.95/6.32 (10292) {G0,W11,D3,L4,V2,M4} { ! point( X ), ! point( Y ), !
% 5.95/6.32 distinct_points( X, Y ), line( line_connecting( X, Y ) ) }.
% 5.95/6.32 (10293) {G0,W11,D3,L4,V2,M4} { ! line( X ), ! line( Y ), !
% 5.95/6.32 convergent_lines( X, Y ), point( intersection_point( X, Y ) ) }.
% 5.95/6.32 (10294) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 5.95/6.32 parallel_through_point( X, Y ) ) }.
% 5.95/6.32 (10295) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 5.95/6.32 orthogonal_through_point( X, Y ) ) }.
% 5.95/6.32 (10296) {G0,W6,D2,L2,V2,M2} { ! equal_points( X, Y ), ! distinct_points( X
% 5.95/6.32 , Y ) }.
% 5.95/6.32 (10297) {G0,W6,D2,L2,V2,M2} { distinct_points( X, Y ), equal_points( X, Y
% 5.95/6.32 ) }.
% 5.95/6.32 (10298) {G0,W6,D2,L2,V2,M2} { ! equal_lines( X, Y ), ! distinct_lines( X,
% 5.95/6.32 Y ) }.
% 5.95/6.32 (10299) {G0,W6,D2,L2,V2,M2} { distinct_lines( X, Y ), equal_lines( X, Y )
% 5.95/6.32 }.
% 5.95/6.32 (10300) {G0,W6,D2,L2,V2,M2} { ! parallel_lines( X, Y ), ! convergent_lines
% 5.95/6.32 ( X, Y ) }.
% 5.95/6.32 (10301) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), parallel_lines( X
% 5.95/6.32 , Y ) }.
% 5.95/6.32 (10302) {G0,W6,D2,L2,V2,M2} { ! incident_point_and_line( X, Y ), !
% 5.95/6.32 apart_point_and_line( X, Y ) }.
% 5.95/6.32 (10303) {G0,W6,D2,L2,V2,M2} { apart_point_and_line( X, Y ),
% 5.95/6.32 incident_point_and_line( X, Y ) }.
% 5.95/6.32 (10304) {G0,W6,D2,L2,V2,M2} { ! orthogonal_lines( X, Y ), !
% 5.95/6.32 unorthogonal_lines( X, Y ) }.
% 5.95/6.32 (10305) {G0,W6,D2,L2,V2,M2} { unorthogonal_lines( X, Y ), orthogonal_lines
% 5.95/6.32 ( X, Y ) }.
% 5.95/6.32 (10306) {G0,W3,D2,L1,V0,M1} { distinct_points( skol1, skol4 ) }.
% 5.95/6.32 (10307) {G0,W3,D2,L1,V0,M1} { convergent_lines( skol2, skol3 ) }.
% 5.95/6.32 (10308) {G0,W3,D2,L1,V0,M1} { incident_point_and_line( skol1, skol2 ) }.
% 5.95/6.32 (10309) {G0,W3,D2,L1,V0,M1} { incident_point_and_line( skol1, skol3 ) }.
% 5.95/6.32 (10310) {G0,W5,D3,L1,V0,M1} { ! equal_points( skol1, intersection_point(
% 5.95/6.32 skol2, skol3 ) ) }.
% 5.95/6.32
% 5.95/6.32
% 5.95/6.32 Total Proof:
% 5.95/6.32
% 5.95/6.32 subsumption: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 5.95/6.32 parent0: (10258) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := X
% 5.95/6.32 end
% 5.95/6.32 permutation0:
% 5.95/6.32 0 ==> 0
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 5.95/6.32 parent0: (10259) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := X
% 5.95/6.32 end
% 5.95/6.32 permutation0:
% 5.95/6.32 0 ==> 0
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 subsumption: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 5.95/6.32 parent0: (10260) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := X
% 5.95/6.32 end
% 5.95/6.32 permutation0:
% 5.95/6.32 0 ==> 0
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 subsumption: (3) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ),
% 5.95/6.32 distinct_points( Y, Z ), ! distinct_points( X, Y ) }.
% 5.95/6.32 parent0: (10261) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ),
% 5.95/6.32 distinct_points( X, Z ), distinct_points( Y, Z ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := X
% 5.95/6.32 Y := Y
% 5.95/6.32 Z := Z
% 5.95/6.32 end
% 5.95/6.32 permutation0:
% 5.95/6.32 0 ==> 2
% 5.95/6.32 1 ==> 0
% 5.95/6.32 2 ==> 1
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 5.95/6.32 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 5.95/6.32 parent0: (10262) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ),
% 5.95/6.32 distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := X
% 5.95/6.32 Y := Y
% 5.95/6.32 Z := Z
% 5.95/6.32 end
% 5.95/6.32 permutation0:
% 5.95/6.32 0 ==> 2
% 5.95/6.32 1 ==> 0
% 5.95/6.32 2 ==> 1
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 subsumption: (8) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 5.95/6.32 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 5.95/6.32 parent0: (10266) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 5.95/6.32 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := X
% 5.95/6.32 Y := Y
% 5.95/6.32 end
% 5.95/6.32 permutation0:
% 5.95/6.32 0 ==> 0
% 5.95/6.32 1 ==> 1
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 subsumption: (9) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 5.95/6.32 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 5.95/6.32 parent0: (10267) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 5.95/6.32 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := X
% 5.95/6.32 Y := Y
% 5.95/6.32 end
% 5.95/6.32 permutation0:
% 5.95/6.32 0 ==> 0
% 5.95/6.32 1 ==> 1
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 subsumption: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), !
% 5.95/6.32 distinct_lines( Z, T ), apart_point_and_line( X, T ),
% 5.95/6.32 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ),
% 5.95/6.32 apart_point_and_line( X, Z ) }.
% 5.95/6.32 parent0: (10268) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), !
% 5.95/6.32 distinct_lines( Z, T ), apart_point_and_line( X, Z ),
% 5.95/6.32 apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 5.95/6.32 apart_point_and_line( Y, T ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := X
% 5.95/6.32 Y := Y
% 5.95/6.32 Z := Z
% 5.95/6.32 T := T
% 5.95/6.32 end
% 5.95/6.32 permutation0:
% 5.95/6.32 0 ==> 0
% 5.95/6.32 1 ==> 1
% 5.95/6.32 2 ==> 5
% 5.95/6.32 3 ==> 2
% 5.95/6.32 4 ==> 3
% 5.95/6.32 5 ==> 4
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 subsumption: (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ),
% 5.95/6.32 convergent_lines( X, Z ), distinct_lines( Y, Z ) }.
% 5.95/6.32 parent0: (10271) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 5.95/6.32 distinct_lines( Y, Z ), convergent_lines( X, Z ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := X
% 5.95/6.32 Y := Y
% 5.95/6.32 Z := Z
% 5.95/6.32 end
% 5.95/6.32 permutation0:
% 5.95/6.32 0 ==> 0
% 5.95/6.32 1 ==> 2
% 5.95/6.32 2 ==> 1
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 subsumption: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 5.95/6.32 distinct_lines( X, Y ) }.
% 5.95/6.32 parent0: (10272) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ),
% 5.95/6.32 convergent_lines( X, Y ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := X
% 5.95/6.32 Y := Y
% 5.95/6.32 end
% 5.95/6.32 permutation0:
% 5.95/6.32 0 ==> 1
% 5.95/6.32 1 ==> 0
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 subsumption: (37) {G0,W6,D2,L2,V2,M1} I { distinct_points( X, Y ),
% 5.95/6.32 equal_points( X, Y ) }.
% 5.95/6.32 parent0: (10297) {G0,W6,D2,L2,V2,M2} { distinct_points( X, Y ),
% 5.95/6.32 equal_points( X, Y ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := X
% 5.95/6.32 Y := Y
% 5.95/6.32 end
% 5.95/6.32 permutation0:
% 5.95/6.32 0 ==> 0
% 5.95/6.32 1 ==> 1
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 subsumption: (42) {G0,W6,D2,L2,V2,M1} I { ! apart_point_and_line( X, Y ), !
% 5.95/6.32 incident_point_and_line( X, Y ) }.
% 5.95/6.32 parent0: (10302) {G0,W6,D2,L2,V2,M2} { ! incident_point_and_line( X, Y ),
% 5.95/6.32 ! apart_point_and_line( X, Y ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := X
% 5.95/6.32 Y := Y
% 5.95/6.32 end
% 5.95/6.32 permutation0:
% 5.95/6.32 0 ==> 1
% 5.95/6.32 1 ==> 0
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 subsumption: (47) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol2, skol3 )
% 5.95/6.32 }.
% 5.95/6.32 parent0: (10307) {G0,W3,D2,L1,V0,M1} { convergent_lines( skol2, skol3 )
% 5.95/6.32 }.
% 5.95/6.32 substitution0:
% 5.95/6.32 end
% 5.95/6.32 permutation0:
% 5.95/6.32 0 ==> 0
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 subsumption: (48) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol1,
% 5.95/6.32 skol2 ) }.
% 5.95/6.32 parent0: (10308) {G0,W3,D2,L1,V0,M1} { incident_point_and_line( skol1,
% 5.95/6.32 skol2 ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 end
% 5.95/6.32 permutation0:
% 5.95/6.32 0 ==> 0
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 subsumption: (49) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol1,
% 5.95/6.32 skol3 ) }.
% 5.95/6.32 parent0: (10309) {G0,W3,D2,L1,V0,M1} { incident_point_and_line( skol1,
% 5.95/6.32 skol3 ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 end
% 5.95/6.32 permutation0:
% 5.95/6.32 0 ==> 0
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 subsumption: (50) {G0,W5,D3,L1,V0,M1} I { ! equal_points( skol1,
% 5.95/6.32 intersection_point( skol2, skol3 ) ) }.
% 5.95/6.32 parent0: (10310) {G0,W5,D3,L1,V0,M1} { ! equal_points( skol1,
% 5.95/6.32 intersection_point( skol2, skol3 ) ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 end
% 5.95/6.32 permutation0:
% 5.95/6.32 0 ==> 0
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 resolution: (10437) {G1,W6,D2,L2,V2,M2} { distinct_points( Y, X ), !
% 5.95/6.32 distinct_points( X, Y ) }.
% 5.95/6.32 parent0[0]: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 5.95/6.32 parent1[0]: (3) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ),
% 5.95/6.32 distinct_points( Y, Z ), ! distinct_points( X, Y ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := X
% 5.95/6.32 end
% 5.95/6.32 substitution1:
% 5.95/6.32 X := X
% 5.95/6.32 Y := Y
% 5.95/6.32 Z := X
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 subsumption: (53) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ),
% 5.95/6.32 distinct_points( X, Y ) }.
% 5.95/6.32 parent0: (10437) {G1,W6,D2,L2,V2,M2} { distinct_points( Y, X ), !
% 5.95/6.32 distinct_points( X, Y ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := Y
% 5.95/6.32 Y := X
% 5.95/6.32 end
% 5.95/6.32 permutation0:
% 5.95/6.32 0 ==> 1
% 5.95/6.32 1 ==> 0
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 resolution: (10439) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 5.95/6.32 distinct_lines( X, Y ) }.
% 5.95/6.32 parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 5.95/6.32 parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 5.95/6.32 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := X
% 5.95/6.32 end
% 5.95/6.32 substitution1:
% 5.95/6.32 X := X
% 5.95/6.32 Y := Y
% 5.95/6.32 Z := X
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 subsumption: (57) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 5.95/6.32 distinct_lines( X, Y ) }.
% 5.95/6.32 parent0: (10439) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 5.95/6.32 distinct_lines( X, Y ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := Y
% 5.95/6.32 Y := X
% 5.95/6.32 end
% 5.95/6.32 permutation0:
% 5.95/6.32 0 ==> 1
% 5.95/6.32 1 ==> 0
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 resolution: (10441) {G1,W9,D2,L3,V3,M3} { distinct_lines( Y, X ),
% 5.95/6.32 distinct_lines( Z, Y ), ! distinct_lines( X, Z ) }.
% 5.95/6.32 parent0[0]: (57) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 5.95/6.32 distinct_lines( X, Y ) }.
% 5.95/6.32 parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 5.95/6.32 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := Y
% 5.95/6.32 Y := X
% 5.95/6.32 end
% 5.95/6.32 substitution1:
% 5.95/6.32 X := X
% 5.95/6.32 Y := Z
% 5.95/6.32 Z := Y
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 subsumption: (58) {G2,W9,D2,L3,V3,M3} R(57,4) { distinct_lines( Z, X ), !
% 5.95/6.32 distinct_lines( Y, Z ), distinct_lines( X, Y ) }.
% 5.95/6.32 parent0: (10441) {G1,W9,D2,L3,V3,M3} { distinct_lines( Y, X ),
% 5.95/6.32 distinct_lines( Z, Y ), ! distinct_lines( X, Z ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := Y
% 5.95/6.32 Y := X
% 5.95/6.32 Z := Z
% 5.95/6.32 end
% 5.95/6.32 permutation0:
% 5.95/6.32 0 ==> 2
% 5.95/6.32 1 ==> 0
% 5.95/6.32 2 ==> 1
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 resolution: (10445) {G1,W9,D2,L3,V3,M3} { distinct_lines( Y, X ),
% 5.95/6.32 distinct_lines( Z, Y ), ! distinct_lines( Z, X ) }.
% 5.95/6.32 parent0[0]: (57) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 5.95/6.32 distinct_lines( X, Y ) }.
% 5.95/6.32 parent1[1]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 5.95/6.32 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := Y
% 5.95/6.32 Y := X
% 5.95/6.32 end
% 5.95/6.32 substitution1:
% 5.95/6.32 X := Z
% 5.95/6.32 Y := X
% 5.95/6.32 Z := Y
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 subsumption: (59) {G2,W9,D2,L3,V3,M3} R(57,4) { distinct_lines( Z, X ), !
% 5.95/6.32 distinct_lines( Z, Y ), distinct_lines( X, Y ) }.
% 5.95/6.32 parent0: (10445) {G1,W9,D2,L3,V3,M3} { distinct_lines( Y, X ),
% 5.95/6.32 distinct_lines( Z, Y ), ! distinct_lines( Z, X ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := Y
% 5.95/6.32 Y := X
% 5.95/6.32 Z := Z
% 5.95/6.32 end
% 5.95/6.32 permutation0:
% 5.95/6.32 0 ==> 2
% 5.95/6.32 1 ==> 0
% 5.95/6.32 2 ==> 1
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 resolution: (10447) {G1,W3,D2,L1,V0,M1} { ! apart_point_and_line( skol1,
% 5.95/6.32 skol2 ) }.
% 5.95/6.32 parent0[1]: (42) {G0,W6,D2,L2,V2,M1} I { ! apart_point_and_line( X, Y ), !
% 5.95/6.32 incident_point_and_line( X, Y ) }.
% 5.95/6.32 parent1[0]: (48) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol1,
% 5.95/6.32 skol2 ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := skol1
% 5.95/6.32 Y := skol2
% 5.95/6.32 end
% 5.95/6.32 substitution1:
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 subsumption: (76) {G1,W3,D2,L1,V0,M1} R(42,48) { ! apart_point_and_line(
% 5.95/6.32 skol1, skol2 ) }.
% 5.95/6.32 parent0: (10447) {G1,W3,D2,L1,V0,M1} { ! apart_point_and_line( skol1,
% 5.95/6.32 skol2 ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 end
% 5.95/6.32 permutation0:
% 5.95/6.32 0 ==> 0
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 resolution: (10448) {G1,W3,D2,L1,V0,M1} { ! apart_point_and_line( skol1,
% 5.95/6.32 skol3 ) }.
% 5.95/6.32 parent0[1]: (42) {G0,W6,D2,L2,V2,M1} I { ! apart_point_and_line( X, Y ), !
% 5.95/6.32 incident_point_and_line( X, Y ) }.
% 5.95/6.32 parent1[0]: (49) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol1,
% 5.95/6.32 skol3 ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := skol1
% 5.95/6.32 Y := skol3
% 5.95/6.32 end
% 5.95/6.32 substitution1:
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 subsumption: (77) {G1,W3,D2,L1,V0,M1} R(42,49) { ! apart_point_and_line(
% 5.95/6.32 skol1, skol3 ) }.
% 5.95/6.32 parent0: (10448) {G1,W3,D2,L1,V0,M1} { ! apart_point_and_line( skol1,
% 5.95/6.32 skol3 ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 end
% 5.95/6.32 permutation0:
% 5.95/6.32 0 ==> 0
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 resolution: (10449) {G1,W5,D3,L1,V0,M1} { distinct_points( skol1,
% 5.95/6.32 intersection_point( skol2, skol3 ) ) }.
% 5.95/6.32 parent0[0]: (50) {G0,W5,D3,L1,V0,M1} I { ! equal_points( skol1,
% 5.95/6.32 intersection_point( skol2, skol3 ) ) }.
% 5.95/6.32 parent1[1]: (37) {G0,W6,D2,L2,V2,M1} I { distinct_points( X, Y ),
% 5.95/6.32 equal_points( X, Y ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 end
% 5.95/6.32 substitution1:
% 5.95/6.32 X := skol1
% 5.95/6.32 Y := intersection_point( skol2, skol3 )
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 subsumption: (78) {G1,W5,D3,L1,V0,M1} R(37,50) { distinct_points( skol1,
% 5.95/6.32 intersection_point( skol2, skol3 ) ) }.
% 5.95/6.32 parent0: (10449) {G1,W5,D3,L1,V0,M1} { distinct_points( skol1,
% 5.95/6.32 intersection_point( skol2, skol3 ) ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 end
% 5.95/6.32 permutation0:
% 5.95/6.32 0 ==> 0
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 resolution: (10450) {G2,W5,D3,L1,V0,M1} { distinct_points(
% 5.95/6.32 intersection_point( skol2, skol3 ), skol1 ) }.
% 5.95/6.32 parent0[0]: (53) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ),
% 5.95/6.32 distinct_points( X, Y ) }.
% 5.95/6.32 parent1[0]: (78) {G1,W5,D3,L1,V0,M1} R(37,50) { distinct_points( skol1,
% 5.95/6.32 intersection_point( skol2, skol3 ) ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := intersection_point( skol2, skol3 )
% 5.95/6.32 Y := skol1
% 5.95/6.32 end
% 5.95/6.32 substitution1:
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 subsumption: (79) {G2,W5,D3,L1,V0,M1} R(78,53) { distinct_points(
% 5.95/6.32 intersection_point( skol2, skol3 ), skol1 ) }.
% 5.95/6.32 parent0: (10450) {G2,W5,D3,L1,V0,M1} { distinct_points( intersection_point
% 5.95/6.32 ( skol2, skol3 ), skol1 ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 end
% 5.95/6.32 permutation0:
% 5.95/6.32 0 ==> 0
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 resolution: (10451) {G1,W22,D3,L6,V4,M6} { ! convergent_lines( X, Y ), !
% 5.95/6.32 distinct_points( intersection_point( X, Y ), Z ), ! distinct_lines( T, Y
% 5.95/6.32 ), apart_point_and_line( Z, T ), apart_point_and_line( Z, Y ),
% 5.95/6.32 apart_point_and_line( intersection_point( X, Y ), T ) }.
% 5.95/6.32 parent0[1]: (9) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 5.95/6.32 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 5.95/6.32 parent1[2]: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), !
% 5.95/6.32 distinct_lines( Z, T ), apart_point_and_line( X, T ),
% 5.95/6.32 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ),
% 5.95/6.32 apart_point_and_line( X, Z ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := X
% 5.95/6.32 Y := Y
% 5.95/6.32 end
% 5.95/6.32 substitution1:
% 5.95/6.32 X := intersection_point( X, Y )
% 5.95/6.32 Y := Z
% 5.95/6.32 Z := T
% 5.95/6.32 T := Y
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 subsumption: (81) {G1,W22,D3,L6,V4,M3} R(10,9) { ! distinct_points(
% 5.95/6.32 intersection_point( X, Y ), Z ), ! distinct_lines( T, Y ), !
% 5.95/6.32 convergent_lines( X, Y ), apart_point_and_line( intersection_point( X, Y
% 5.95/6.32 ), T ), apart_point_and_line( Z, T ), apart_point_and_line( Z, Y ) }.
% 5.95/6.32 parent0: (10451) {G1,W22,D3,L6,V4,M6} { ! convergent_lines( X, Y ), !
% 5.95/6.32 distinct_points( intersection_point( X, Y ), Z ), ! distinct_lines( T, Y
% 5.95/6.32 ), apart_point_and_line( Z, T ), apart_point_and_line( Z, Y ),
% 5.95/6.32 apart_point_and_line( intersection_point( X, Y ), T ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := X
% 5.95/6.32 Y := Y
% 5.95/6.32 Z := Z
% 5.95/6.32 T := T
% 5.95/6.32 end
% 5.95/6.32 permutation0:
% 5.95/6.32 0 ==> 2
% 5.95/6.32 1 ==> 0
% 5.95/6.32 2 ==> 1
% 5.95/6.32 3 ==> 4
% 5.95/6.32 4 ==> 5
% 5.95/6.32 5 ==> 3
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 resolution: (10460) {G1,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), !
% 5.95/6.32 distinct_lines( Y, X ) }.
% 5.95/6.32 parent0[1]: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 5.95/6.32 distinct_lines( X, Y ) }.
% 5.95/6.32 parent1[1]: (57) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 5.95/6.32 distinct_lines( X, Y ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := X
% 5.95/6.32 Y := Y
% 5.95/6.32 end
% 5.95/6.32 substitution1:
% 5.95/6.32 X := X
% 5.95/6.32 Y := Y
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 subsumption: (146) {G2,W6,D2,L2,V2,M1} R(14,57) { convergent_lines( X, Y )
% 5.95/6.32 , ! distinct_lines( Y, X ) }.
% 5.95/6.32 parent0: (10460) {G1,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), !
% 5.95/6.32 distinct_lines( Y, X ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := X
% 5.95/6.32 Y := Y
% 5.95/6.32 end
% 5.95/6.32 permutation0:
% 5.95/6.32 0 ==> 0
% 5.95/6.32 1 ==> 1
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 resolution: (10461) {G3,W9,D2,L3,V3,M3} { convergent_lines( X, Y ), !
% 5.95/6.32 distinct_lines( Z, Y ), distinct_lines( X, Z ) }.
% 5.95/6.32 parent0[1]: (146) {G2,W6,D2,L2,V2,M1} R(14,57) { convergent_lines( X, Y ),
% 5.95/6.32 ! distinct_lines( Y, X ) }.
% 5.95/6.32 parent1[0]: (58) {G2,W9,D2,L3,V3,M3} R(57,4) { distinct_lines( Z, X ), !
% 5.95/6.32 distinct_lines( Y, Z ), distinct_lines( X, Y ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := X
% 5.95/6.32 Y := Y
% 5.95/6.32 end
% 5.95/6.32 substitution1:
% 5.95/6.32 X := X
% 5.95/6.32 Y := Z
% 5.95/6.32 Z := Y
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 subsumption: (511) {G3,W9,D2,L3,V3,M2} R(58,146) { convergent_lines( Z, Y )
% 5.95/6.32 , ! distinct_lines( X, Y ), distinct_lines( Z, X ) }.
% 5.95/6.32 parent0: (10461) {G3,W9,D2,L3,V3,M3} { convergent_lines( X, Y ), !
% 5.95/6.32 distinct_lines( Z, Y ), distinct_lines( X, Z ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := Z
% 5.95/6.32 Y := Y
% 5.95/6.32 Z := X
% 5.95/6.32 end
% 5.95/6.32 permutation0:
% 5.95/6.32 0 ==> 0
% 5.95/6.32 1 ==> 1
% 5.95/6.32 2 ==> 2
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 resolution: (10463) {G3,W9,D2,L3,V3,M3} { convergent_lines( X, Y ), !
% 5.95/6.32 distinct_lines( Y, Z ), distinct_lines( X, Z ) }.
% 5.95/6.32 parent0[1]: (146) {G2,W6,D2,L2,V2,M1} R(14,57) { convergent_lines( X, Y ),
% 5.95/6.32 ! distinct_lines( Y, X ) }.
% 5.95/6.32 parent1[0]: (59) {G2,W9,D2,L3,V3,M3} R(57,4) { distinct_lines( Z, X ), !
% 5.95/6.32 distinct_lines( Z, Y ), distinct_lines( X, Y ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := X
% 5.95/6.32 Y := Y
% 5.95/6.32 end
% 5.95/6.32 substitution1:
% 5.95/6.32 X := X
% 5.95/6.32 Y := Z
% 5.95/6.32 Z := Y
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 subsumption: (529) {G3,W9,D2,L3,V3,M2} R(59,146) { convergent_lines( Z, X )
% 5.95/6.32 , ! distinct_lines( X, Y ), distinct_lines( Z, Y ) }.
% 5.95/6.32 parent0: (10463) {G3,W9,D2,L3,V3,M3} { convergent_lines( X, Y ), !
% 5.95/6.32 distinct_lines( Y, Z ), distinct_lines( X, Z ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := Z
% 5.95/6.32 Y := X
% 5.95/6.32 Z := Y
% 5.95/6.32 end
% 5.95/6.32 permutation0:
% 5.95/6.32 0 ==> 0
% 5.95/6.32 1 ==> 1
% 5.95/6.32 2 ==> 2
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 resolution: (10465) {G1,W12,D2,L4,V4,M4} { convergent_lines( X, Y ),
% 5.95/6.32 distinct_lines( X, Z ), ! convergent_lines( T, Z ), convergent_lines( T,
% 5.95/6.32 Y ) }.
% 5.95/6.32 parent0[1]: (511) {G3,W9,D2,L3,V3,M2} R(58,146) { convergent_lines( Z, Y )
% 5.95/6.32 , ! distinct_lines( X, Y ), distinct_lines( Z, X ) }.
% 5.95/6.32 parent1[2]: (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ),
% 5.95/6.32 convergent_lines( X, Z ), distinct_lines( Y, Z ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := Z
% 5.95/6.32 Y := Y
% 5.95/6.32 Z := X
% 5.95/6.32 end
% 5.95/6.32 substitution1:
% 5.95/6.32 X := T
% 5.95/6.32 Y := Z
% 5.95/6.32 Z := Y
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 subsumption: (702) {G4,W12,D2,L4,V4,M1} R(511,13) { convergent_lines( X, Y
% 5.95/6.32 ), ! convergent_lines( T, Z ), convergent_lines( T, Y ), distinct_lines
% 5.95/6.32 ( X, Z ) }.
% 5.95/6.32 parent0: (10465) {G1,W12,D2,L4,V4,M4} { convergent_lines( X, Y ),
% 5.95/6.32 distinct_lines( X, Z ), ! convergent_lines( T, Z ), convergent_lines( T,
% 5.95/6.32 Y ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := X
% 5.95/6.32 Y := Y
% 5.95/6.32 Z := Z
% 5.95/6.32 T := T
% 5.95/6.32 end
% 5.95/6.32 permutation0:
% 5.95/6.32 0 ==> 0
% 5.95/6.32 1 ==> 3
% 5.95/6.32 2 ==> 1
% 5.95/6.32 3 ==> 2
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 factor: (10467) {G4,W9,D2,L3,V3,M3} { convergent_lines( X, Y ), !
% 5.95/6.32 convergent_lines( X, Z ), distinct_lines( X, Z ) }.
% 5.95/6.32 parent0[0, 2]: (702) {G4,W12,D2,L4,V4,M1} R(511,13) { convergent_lines( X,
% 5.95/6.32 Y ), ! convergent_lines( T, Z ), convergent_lines( T, Y ), distinct_lines
% 5.95/6.32 ( X, Z ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := X
% 5.95/6.32 Y := Y
% 5.95/6.32 Z := Z
% 5.95/6.32 T := X
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 subsumption: (703) {G5,W9,D2,L3,V3,M1} F(702) { convergent_lines( X, Y ), !
% 5.95/6.32 convergent_lines( X, Z ), distinct_lines( X, Z ) }.
% 5.95/6.32 parent0: (10467) {G4,W9,D2,L3,V3,M3} { convergent_lines( X, Y ), !
% 5.95/6.32 convergent_lines( X, Z ), distinct_lines( X, Z ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := X
% 5.95/6.32 Y := Y
% 5.95/6.32 Z := Z
% 5.95/6.32 end
% 5.95/6.32 permutation0:
% 5.95/6.32 0 ==> 0
% 5.95/6.32 1 ==> 1
% 5.95/6.32 2 ==> 2
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 resolution: (10470) {G4,W12,D2,L4,V4,M4} { convergent_lines( X, Y ),
% 5.95/6.32 distinct_lines( X, Z ), convergent_lines( Y, T ), ! convergent_lines( Y,
% 5.95/6.32 Z ) }.
% 5.95/6.32 parent0[1]: (529) {G3,W9,D2,L3,V3,M2} R(59,146) { convergent_lines( Z, X )
% 5.95/6.32 , ! distinct_lines( X, Y ), distinct_lines( Z, Y ) }.
% 5.95/6.32 parent1[2]: (703) {G5,W9,D2,L3,V3,M1} F(702) { convergent_lines( X, Y ), !
% 5.95/6.32 convergent_lines( X, Z ), distinct_lines( X, Z ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := Y
% 5.95/6.32 Y := Z
% 5.95/6.32 Z := X
% 5.95/6.32 end
% 5.95/6.32 substitution1:
% 5.95/6.32 X := Y
% 5.95/6.32 Y := T
% 5.95/6.32 Z := Z
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 subsumption: (731) {G6,W12,D2,L4,V4,M1} R(703,529) { convergent_lines( X, Y
% 5.95/6.32 ), ! convergent_lines( X, Z ), convergent_lines( T, X ), distinct_lines
% 5.95/6.32 ( T, Z ) }.
% 5.95/6.32 parent0: (10470) {G4,W12,D2,L4,V4,M4} { convergent_lines( X, Y ),
% 5.95/6.32 distinct_lines( X, Z ), convergent_lines( Y, T ), ! convergent_lines( Y,
% 5.95/6.32 Z ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := T
% 5.95/6.32 Y := X
% 5.95/6.32 Z := Z
% 5.95/6.32 T := Y
% 5.95/6.32 end
% 5.95/6.32 permutation0:
% 5.95/6.32 0 ==> 2
% 5.95/6.32 1 ==> 3
% 5.95/6.32 2 ==> 0
% 5.95/6.32 3 ==> 1
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 factor: (10472) {G6,W9,D2,L3,V2,M3} { convergent_lines( X, X ), !
% 5.95/6.32 convergent_lines( X, Y ), distinct_lines( X, Y ) }.
% 5.95/6.32 parent0[0, 2]: (731) {G6,W12,D2,L4,V4,M1} R(703,529) { convergent_lines( X
% 5.95/6.32 , Y ), ! convergent_lines( X, Z ), convergent_lines( T, X ),
% 5.95/6.32 distinct_lines( T, Z ) }.
% 5.95/6.32 substitution0:
% 5.95/6.32 X := X
% 5.95/6.32 Y := X
% 5.95/6.32 Z := Y
% 5.95/6.32 T := X
% 5.95/6.32 end
% 5.95/6.32
% 5.95/6.32 resolution: (10473) {G1,W6,D2,L2,V2,M2} { ! convergent_lines( X, Y ),
% 5.95/6.32 distinct_lines( X, Y ) }.
% 5.95/6.32 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 5.95/6.33 parent1[0]: (10472) {G6,W9,D2,L3,V2,M3} { convergent_lines( X, X ), !
% 5.95/6.33 convergent_lines( X, Y ), distinct_lines( X, Y ) }.
% 5.95/6.33 substitution0:
% 5.95/6.33 X := X
% 5.95/6.33 end
% 5.95/6.33 substitution1:
% 5.95/6.33 X := X
% 5.95/6.33 Y := Y
% 5.95/6.33 end
% 5.95/6.33
% 5.95/6.33 subsumption: (738) {G7,W6,D2,L2,V2,M1} F(731);r(2) { ! convergent_lines( X
% 5.95/6.33 , Y ), distinct_lines( X, Y ) }.
% 5.95/6.33 parent0: (10473) {G1,W6,D2,L2,V2,M2} { ! convergent_lines( X, Y ),
% 5.95/6.33 distinct_lines( X, Y ) }.
% 5.95/6.33 substitution0:
% 5.95/6.33 X := X
% 5.95/6.33 Y := Y
% 5.95/6.33 end
% 5.95/6.33 permutation0:
% 5.95/6.33 0 ==> 0
% 5.95/6.33 1 ==> 1
% 5.95/6.33 end
% 5.95/6.33
% 5.95/6.33 resolution: (10474) {G1,W20,D3,L6,V3,M6} { ! convergent_lines( X, Y ), !
% 5.95/6.33 distinct_points( intersection_point( X, Y ), Z ), ! distinct_lines( X, Y
% 5.95/6.33 ), ! convergent_lines( X, Y ), apart_point_and_line( Z, X ),
% 5.95/6.33 apart_point_and_line( Z, Y ) }.
% 5.95/6.33 parent0[1]: (8) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 5.95/6.33 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 5.95/6.33 parent1[3]: (81) {G1,W22,D3,L6,V4,M3} R(10,9) { ! distinct_points(
% 5.95/6.33 intersection_point( X, Y ), Z ), ! distinct_lines( T, Y ), !
% 5.95/6.33 convergent_lines( X, Y ), apart_point_and_line( intersection_point( X, Y
% 5.95/6.33 ), T ), apart_point_and_line( Z, T ), apart_point_and_line( Z, Y ) }.
% 5.95/6.33 substitution0:
% 5.95/6.33 X := X
% 5.95/6.33 Y := Y
% 5.95/6.33 end
% 5.95/6.33 substitution1:
% 5.95/6.33 X := X
% 5.95/6.33 Y := Y
% 5.95/6.33 Z := Z
% 5.95/6.33 T := X
% 5.95/6.33 end
% 5.95/6.33
% 5.95/6.33 resolution: (10511) {G2,W20,D3,L6,V3,M6} { ! convergent_lines( X, Y ), !
% 5.95/6.33 distinct_points( intersection_point( X, Y ), Z ), ! convergent_lines( X,
% 5.95/6.33 Y ), apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), !
% 5.95/6.33 convergent_lines( X, Y ) }.
% 5.95/6.33 parent0[2]: (10474) {G1,W20,D3,L6,V3,M6} { ! convergent_lines( X, Y ), !
% 5.95/6.33 distinct_points( intersection_point( X, Y ), Z ), ! distinct_lines( X, Y
% 5.95/6.33 ), ! convergent_lines( X, Y ), apart_point_and_line( Z, X ),
% 5.95/6.33 apart_point_and_line( Z, Y ) }.
% 5.95/6.33 parent1[1]: (738) {G7,W6,D2,L2,V2,M1} F(731);r(2) { ! convergent_lines( X,
% 5.95/6.33 Y ), distinct_lines( X, Y ) }.
% 5.95/6.33 substitution0:
% 5.95/6.33 X := X
% 5.95/6.33 Y := Y
% 5.95/6.33 Z := Z
% 5.95/6.33 end
% 5.95/6.33 substitution1:
% 5.95/6.33 X := X
% 5.95/6.33 Y := Y
% 5.95/6.33 end
% 5.95/6.33
% 5.95/6.33 factor: (10512) {G2,W17,D3,L5,V3,M5} { ! convergent_lines( X, Y ), !
% 5.95/6.33 distinct_points( intersection_point( X, Y ), Z ), apart_point_and_line( Z
% 5.95/6.33 , X ), apart_point_and_line( Z, Y ), ! convergent_lines( X, Y ) }.
% 5.95/6.33 parent0[0, 2]: (10511) {G2,W20,D3,L6,V3,M6} { ! convergent_lines( X, Y ),
% 5.95/6.33 ! distinct_points( intersection_point( X, Y ), Z ), ! convergent_lines( X
% 5.95/6.33 , Y ), apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), !
% 5.95/6.33 convergent_lines( X, Y ) }.
% 5.95/6.33 substitution0:
% 5.95/6.33 X := X
% 5.95/6.33 Y := Y
% 5.95/6.33 Z := Z
% 5.95/6.33 end
% 5.95/6.33
% 5.95/6.33 factor: (10513) {G2,W14,D3,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 5.95/6.33 distinct_points( intersection_point( X, Y ), Z ), apart_point_and_line( Z
% 5.95/6.33 , X ), apart_point_and_line( Z, Y ) }.
% 5.95/6.33 parent0[0, 4]: (10512) {G2,W17,D3,L5,V3,M5} { ! convergent_lines( X, Y ),
% 5.95/6.33 ! distinct_points( intersection_point( X, Y ), Z ), apart_point_and_line
% 5.95/6.33 ( Z, X ), apart_point_and_line( Z, Y ), ! convergent_lines( X, Y ) }.
% 5.95/6.33 substitution0:
% 5.95/6.33 X := X
% 5.95/6.33 Y := Y
% 5.95/6.33 Z := Z
% 5.95/6.33 end
% 5.95/6.33
% 5.95/6.33 subsumption: (917) {G8,W14,D3,L4,V3,M2} R(81,8);f;r(738) { !
% 5.95/6.33 convergent_lines( X, Y ), ! distinct_points( intersection_point( X, Y ),
% 5.95/6.33 Z ), apart_point_and_line( Z, Y ), apart_point_and_line( Z, X ) }.
% 5.95/6.33 parent0: (10513) {G2,W14,D3,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 5.95/6.33 distinct_points( intersection_point( X, Y ), Z ), apart_point_and_line( Z
% 5.95/6.33 , X ), apart_point_and_line( Z, Y ) }.
% 5.95/6.33 substitution0:
% 5.95/6.33 X := X
% 5.95/6.33 Y := Y
% 5.95/6.33 Z := Z
% 5.95/6.33 end
% 5.95/6.33 permutation0:
% 5.95/6.33 0 ==> 0
% 5.95/6.33 1 ==> 1
% 5.95/6.33 2 ==> 3
% 5.95/6.33 3 ==> 2
% 5.95/6.33 end
% 5.95/6.33
% 5.95/6.33 resolution: (10515) {G2,W11,D3,L3,V1,M3} { ! convergent_lines( X, skol3 )
% 5.95/6.33 , ! distinct_points( intersection_point( X, skol3 ), skol1 ),
% 5.95/6.33 apart_point_and_line( skol1, X ) }.
% 5.95/6.33 parent0[0]: (77) {G1,W3,D2,L1,V0,M1} R(42,49) { ! apart_point_and_line(
% 5.95/6.33 skol1, skol3 ) }.
% 5.95/6.33 parent1[2]: (917) {G8,W14,D3,L4,V3,M2} R(81,8);f;r(738) { !
% 5.95/6.33 convergent_lines( X, Y ), ! distinct_points( intersection_point( X, Y ),
% 5.95/6.33 Z ), apart_point_and_line( Z, Y ), apart_point_and_line( Z, X ) }.
% 5.95/6.33 substitution0:
% 5.95/6.33 end
% 5.95/6.33 substitution1:
% 5.95/6.33 X := X
% 5.95/6.33 Y := skol3
% 5.95/6.33 Z := skol1
% 5.95/6.33 end
% 5.95/6.33
% 5.95/6.33 subsumption: (10215) {G9,W11,D3,L3,V1,M1} R(917,77) { ! convergent_lines( X
% 5.95/6.33 , skol3 ), ! distinct_points( intersection_point( X, skol3 ), skol1 ),
% 5.95/6.33 apart_point_and_line( skol1, X ) }.
% 5.95/6.33 parent0: (10515) {G2,W11,D3,L3,V1,M3} { ! convergent_lines( X, skol3 ), !
% 5.95/6.33 distinct_points( intersection_point( X, skol3 ), skol1 ),
% 5.95/6.33 apart_point_and_line( skol1, X ) }.
% 5.95/6.33 substitution0:
% 5.95/6.33 X := X
% 5.95/6.33 end
% 5.95/6.33 permutation0:
% 5.95/6.33 0 ==> 0
% 5.95/6.33 1 ==> 1
% 5.95/6.33 2 ==> 2
% 5.95/6.33 end
% 5.95/6.33
% 5.95/6.33 resolution: (10517) {G2,W8,D3,L2,V0,M2} { ! convergent_lines( skol2, skol3
% 5.95/6.33 ), ! distinct_points( intersection_point( skol2, skol3 ), skol1 ) }.
% 5.95/6.33 parent0[0]: (76) {G1,W3,D2,L1,V0,M1} R(42,48) { ! apart_point_and_line(
% 5.95/6.33 skol1, skol2 ) }.
% 5.95/6.33 parent1[2]: (10215) {G9,W11,D3,L3,V1,M1} R(917,77) { ! convergent_lines( X
% 5.95/6.33 , skol3 ), ! distinct_points( intersection_point( X, skol3 ), skol1 ),
% 5.95/6.33 apart_point_and_line( skol1, X ) }.
% 5.95/6.33 substitution0:
% 5.95/6.33 end
% 5.95/6.33 substitution1:
% 5.95/6.33 X := skol2
% 5.95/6.33 end
% 5.95/6.33
% 5.95/6.33 resolution: (10518) {G1,W5,D3,L1,V0,M1} { ! distinct_points(
% 5.95/6.33 intersection_point( skol2, skol3 ), skol1 ) }.
% 5.95/6.33 parent0[0]: (10517) {G2,W8,D3,L2,V0,M2} { ! convergent_lines( skol2, skol3
% 5.95/6.33 ), ! distinct_points( intersection_point( skol2, skol3 ), skol1 ) }.
% 5.95/6.33 parent1[0]: (47) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol2, skol3 )
% 5.95/6.33 }.
% 5.95/6.33 substitution0:
% 5.95/6.33 end
% 5.95/6.33 substitution1:
% 5.95/6.33 end
% 5.95/6.33
% 5.95/6.33 subsumption: (10251) {G10,W5,D3,L1,V0,M1} R(10215,76);r(47) { !
% 5.95/6.33 distinct_points( intersection_point( skol2, skol3 ), skol1 ) }.
% 5.95/6.33 parent0: (10518) {G1,W5,D3,L1,V0,M1} { ! distinct_points(
% 5.95/6.33 intersection_point( skol2, skol3 ), skol1 ) }.
% 5.95/6.33 substitution0:
% 5.95/6.33 end
% 5.95/6.33 permutation0:
% 5.95/6.33 0 ==> 0
% 5.95/6.33 end
% 5.95/6.33
% 5.95/6.33 resolution: (10519) {G3,W0,D0,L0,V0,M0} { }.
% 5.95/6.33 parent0[0]: (10251) {G10,W5,D3,L1,V0,M1} R(10215,76);r(47) { !
% 5.95/6.33 distinct_points( intersection_point( skol2, skol3 ), skol1 ) }.
% 5.95/6.33 parent1[0]: (79) {G2,W5,D3,L1,V0,M1} R(78,53) { distinct_points(
% 5.95/6.33 intersection_point( skol2, skol3 ), skol1 ) }.
% 5.95/6.33 substitution0:
% 5.95/6.33 end
% 5.95/6.33 substitution1:
% 5.95/6.33 end
% 5.95/6.33
% 5.95/6.33 subsumption: (10256) {G11,W0,D0,L0,V0,M0} S(10251);r(79) { }.
% 5.95/6.33 parent0: (10519) {G3,W0,D0,L0,V0,M0} { }.
% 5.95/6.33 substitution0:
% 5.95/6.33 end
% 5.95/6.33 permutation0:
% 5.95/6.33 end
% 5.95/6.33
% 5.95/6.33 Proof check complete!
% 5.95/6.33
% 5.95/6.33 Memory use:
% 5.95/6.33
% 5.95/6.33 space for terms: 148944
% 5.95/6.33 space for clauses: 468534
% 5.95/6.33
% 5.95/6.33
% 5.95/6.33 clauses generated: 851211
% 5.95/6.33 clauses kept: 10257
% 5.95/6.33 clauses selected: 2106
% 5.95/6.33 clauses deleted: 24
% 5.95/6.33 clauses inuse deleted: 2
% 5.95/6.33
% 5.95/6.33 subsentry: 9409279
% 5.95/6.33 literals s-matched: 3677411
% 5.95/6.33 literals matched: 3676867
% 5.95/6.33 full subsumption: 2501682
% 5.95/6.33
% 5.95/6.33 checksum: 197970590
% 5.95/6.33
% 5.95/6.33
% 5.95/6.33 Bliksem ended
%------------------------------------------------------------------------------