TSTP Solution File: GEO172+3 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO172+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Sat Jul 16 02:52:13 EDT 2022
% Result : Theorem 6.55s 6.93s
% Output : Refutation 6.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO172+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : bliksem %s
% 0.14/0.33 % Computer : n016.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % DateTime : Sat Jun 18 01:15:21 EDT 2022
% 0.14/0.33 % CPUTime :
% 6.55/6.93 *** allocated 10000 integers for termspace/termends
% 6.55/6.93 *** allocated 10000 integers for clauses
% 6.55/6.93 *** allocated 10000 integers for justifications
% 6.55/6.93 Bliksem 1.12
% 6.55/6.93
% 6.55/6.93
% 6.55/6.93 Automatic Strategy Selection
% 6.55/6.93
% 6.55/6.93
% 6.55/6.93 Clauses:
% 6.55/6.93
% 6.55/6.93 { ! distinct_points( X, X ) }.
% 6.55/6.93 { ! distinct_lines( X, X ) }.
% 6.55/6.93 { ! convergent_lines( X, X ) }.
% 6.55/6.93 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 6.55/6.93 ) }.
% 6.55/6.93 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 6.55/6.93 }.
% 6.55/6.93 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 6.55/6.93 , Z ) }.
% 6.55/6.93 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 6.55/6.93 , Y ) ) }.
% 6.55/6.93 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 6.55/6.93 , Y ) ) }.
% 6.55/6.93 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 6.55/6.93 , Y ), X ) }.
% 6.55/6.93 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 6.55/6.93 , Y ), Y ) }.
% 6.55/6.93 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 6.55/6.93 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 6.55/6.93 apart_point_and_line( Y, T ) }.
% 6.55/6.93 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 6.55/6.93 apart_point_and_line( Z, Y ) }.
% 6.55/6.93 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 6.55/6.93 apart_point_and_line( X, Z ) }.
% 6.55/6.93 { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X,
% 6.55/6.93 Z ) }.
% 6.55/6.93 { ! distinct_lines( X, Y ), convergent_lines( X, Y ) }.
% 6.55/6.93 { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 6.55/6.93 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 6.55/6.93 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 6.55/6.93 apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 6.55/6.93 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 6.55/6.93 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 6.55/6.93 , convergent_lines( Y, Z ) }.
% 6.55/6.93 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 6.55/6.93 , unorthogonal_lines( Y, Z ) }.
% 6.55/6.93 { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 6.55/6.93 { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 6.55/6.93 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 6.55/6.93 }.
% 6.55/6.93 { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 6.55/6.93 { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 6.55/6.93 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 6.55/6.93 apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ),
% 6.55/6.93 unorthogonal_lines( Y, T ) }.
% 6.55/6.93 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 6.55/6.93 { alpha2( X, Z ), convergent_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 6.55/6.93 unorthogonal_lines( X, Y ) }.
% 6.55/6.93 { alpha2( X, Z ), unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 6.55/6.93 unorthogonal_lines( X, Y ) }.
% 6.55/6.93 { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 6.55/6.93 { ! alpha2( X, Y ), unorthogonal_lines( Y, X ) }.
% 6.55/6.93 { ! convergent_lines( Y, X ), ! unorthogonal_lines( Y, X ), alpha2( X, Y )
% 6.55/6.93 }.
% 6.55/6.93 { unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ), !
% 6.55/6.93 convergent_lines( X, Y ) }.
% 6.55/6.93 { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line(
% 6.55/6.93 line_connecting( X, Y ) ) }.
% 6.55/6.93 { ! line( X ), ! line( Y ), ! convergent_lines( X, Y ), point(
% 6.55/6.93 intersection_point( X, Y ) ) }.
% 6.55/6.93 { ! line( X ), ! point( Y ), line( parallel_through_point( X, Y ) ) }.
% 6.55/6.93 { ! line( X ), ! point( Y ), line( orthogonal_through_point( X, Y ) ) }.
% 6.55/6.93 { ! equal_points( X, Y ), ! distinct_points( X, Y ) }.
% 6.55/6.93 { distinct_points( X, Y ), equal_points( X, Y ) }.
% 6.55/6.93 { ! equal_lines( X, Y ), ! distinct_lines( X, Y ) }.
% 6.55/6.93 { distinct_lines( X, Y ), equal_lines( X, Y ) }.
% 6.55/6.93 { ! parallel_lines( X, Y ), ! convergent_lines( X, Y ) }.
% 6.55/6.93 { convergent_lines( X, Y ), parallel_lines( X, Y ) }.
% 6.55/6.93 { ! incident_point_and_line( X, Y ), ! apart_point_and_line( X, Y ) }.
% 6.55/6.93 { apart_point_and_line( X, Y ), incident_point_and_line( X, Y ) }.
% 6.55/6.93 { ! orthogonal_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 6.55/6.93 { unorthogonal_lines( X, Y ), orthogonal_lines( X, Y ) }.
% 6.55/6.93 { convergent_lines( skol1, skol2 ) }.
% 6.55/6.93 { incident_point_and_line( skol3, skol1 ) }.
% 6.55/6.93 { incident_point_and_line( skol3, skol2 ) }.
% 6.55/6.93 { ! equal_points( skol3, intersection_point( skol1, skol2 ) ) }.
% 6.55/6.93
% 6.55/6.93 percentage equality = 0.000000, percentage horn = 0.620000
% 6.55/6.93 This a non-horn, non-equality problem
% 6.55/6.93
% 6.55/6.93
% 6.55/6.93 Options Used:
% 6.55/6.93
% 6.55/6.93 useres = 1
% 6.55/6.93 useparamod = 0
% 6.55/6.93 useeqrefl = 0
% 6.55/6.93 useeqfact = 0
% 6.55/6.93 usefactor = 1
% 6.55/6.93 usesimpsplitting = 0
% 6.55/6.93 usesimpdemod = 0
% 6.55/6.93 usesimpres = 3
% 6.55/6.93
% 6.55/6.93 resimpinuse = 1000
% 6.55/6.93 resimpclauses = 20000
% 6.55/6.93 substype = standard
% 6.55/6.93 backwardsubs = 1
% 6.55/6.93 selectoldest = 5
% 6.55/6.93
% 6.55/6.93 litorderings [0] = split
% 6.55/6.93 litorderings [1] = liftord
% 6.55/6.93
% 6.55/6.93 termordering = none
% 6.55/6.93
% 6.55/6.93 litapriori = 1
% 6.55/6.93 termapriori = 0
% 6.55/6.93 litaposteriori = 0
% 6.55/6.93 termaposteriori = 0
% 6.55/6.93 demodaposteriori = 0
% 6.55/6.93 ordereqreflfact = 0
% 6.55/6.93
% 6.55/6.93 litselect = none
% 6.55/6.93
% 6.55/6.93 maxweight = 15
% 6.55/6.93 maxdepth = 30000
% 6.55/6.93 maxlength = 115
% 6.55/6.93 maxnrvars = 195
% 6.55/6.93 excuselevel = 1
% 6.55/6.93 increasemaxweight = 1
% 6.55/6.93
% 6.55/6.93 maxselected = 10000000
% 6.55/6.93 maxnrclauses = 10000000
% 6.55/6.93
% 6.55/6.93 showgenerated = 0
% 6.55/6.93 showkept = 0
% 6.55/6.93 showselected = 0
% 6.55/6.93 showdeleted = 0
% 6.55/6.93 showresimp = 1
% 6.55/6.93 showstatus = 2000
% 6.55/6.93
% 6.55/6.93 prologoutput = 0
% 6.55/6.93 nrgoals = 5000000
% 6.55/6.93 totalproof = 1
% 6.55/6.93
% 6.55/6.93 Symbols occurring in the translation:
% 6.55/6.93
% 6.55/6.93 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 6.55/6.93 . [1, 2] (w:1, o:26, a:1, s:1, b:0),
% 6.55/6.93 ! [4, 1] (w:0, o:19, a:1, s:1, b:0),
% 6.55/6.93 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 6.55/6.93 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 6.55/6.93 distinct_points [36, 2] (w:1, o:51, a:1, s:1, b:0),
% 6.55/6.93 distinct_lines [37, 2] (w:1, o:52, a:1, s:1, b:0),
% 6.55/6.93 convergent_lines [38, 2] (w:1, o:50, a:1, s:1, b:0),
% 6.55/6.93 line_connecting [41, 2] (w:1, o:53, a:1, s:1, b:0),
% 6.55/6.93 apart_point_and_line [42, 2] (w:1, o:54, a:1, s:1, b:0),
% 6.55/6.93 intersection_point [43, 2] (w:1, o:55, a:1, s:1, b:0),
% 6.55/6.93 parallel_through_point [46, 2] (w:1, o:58, a:1, s:1, b:0),
% 6.55/6.93 unorthogonal_lines [49, 2] (w:1, o:59, a:1, s:1, b:0),
% 6.55/6.93 orthogonal_through_point [52, 2] (w:1, o:56, a:1, s:1, b:0),
% 6.55/6.93 point [54, 1] (w:1, o:24, a:1, s:1, b:0),
% 6.55/6.93 line [55, 1] (w:1, o:25, a:1, s:1, b:0),
% 6.55/6.93 equal_points [56, 2] (w:1, o:60, a:1, s:1, b:0),
% 6.55/6.93 equal_lines [57, 2] (w:1, o:61, a:1, s:1, b:0),
% 6.55/6.93 parallel_lines [58, 2] (w:1, o:62, a:1, s:1, b:0),
% 6.55/6.93 incident_point_and_line [59, 2] (w:1, o:63, a:1, s:1, b:0),
% 6.55/6.93 orthogonal_lines [60, 2] (w:1, o:57, a:1, s:1, b:0),
% 6.55/6.93 alpha1 [61, 2] (w:1, o:64, a:1, s:1, b:0),
% 6.55/6.93 alpha2 [62, 2] (w:1, o:65, a:1, s:1, b:0),
% 6.55/6.93 skol1 [63, 0] (w:1, o:16, a:1, s:1, b:0),
% 6.55/6.93 skol2 [64, 0] (w:1, o:17, a:1, s:1, b:0),
% 6.55/6.93 skol3 [65, 0] (w:1, o:18, a:1, s:1, b:0).
% 6.55/6.93
% 6.55/6.93
% 6.55/6.93 Starting Search:
% 6.55/6.93
% 6.55/6.93 *** allocated 15000 integers for clauses
% 6.55/6.93 *** allocated 22500 integers for clauses
% 6.55/6.93 *** allocated 33750 integers for clauses
% 6.55/6.93 *** allocated 15000 integers for termspace/termends
% 6.55/6.93 *** allocated 50625 integers for clauses
% 6.55/6.93 Resimplifying inuse:
% 6.55/6.93 Done
% 6.55/6.93
% 6.55/6.93 *** allocated 22500 integers for termspace/termends
% 6.55/6.93 *** allocated 75937 integers for clauses
% 6.55/6.93 *** allocated 33750 integers for termspace/termends
% 6.55/6.93 *** allocated 113905 integers for clauses
% 6.55/6.93
% 6.55/6.93 Intermediate Status:
% 6.55/6.93 Generated: 15809
% 6.55/6.93 Kept: 2001
% 6.55/6.93 Inuse: 343
% 6.55/6.93 Deleted: 2
% 6.55/6.93 Deletedinuse: 2
% 6.55/6.93
% 6.55/6.93 Resimplifying inuse:
% 6.55/6.93 Done
% 6.55/6.93
% 6.55/6.93 *** allocated 50625 integers for termspace/termends
% 6.55/6.93 *** allocated 170857 integers for clauses
% 6.55/6.93 Resimplifying inuse:
% 6.55/6.93 Done
% 6.55/6.93
% 6.55/6.93 *** allocated 75937 integers for termspace/termends
% 6.55/6.93
% 6.55/6.93 Intermediate Status:
% 6.55/6.93 Generated: 40069
% 6.55/6.93 Kept: 4061
% 6.55/6.93 Inuse: 486
% 6.55/6.93 Deleted: 5
% 6.55/6.93 Deletedinuse: 2
% 6.55/6.93
% 6.55/6.93 Resimplifying inuse:
% 6.55/6.93 Done
% 6.55/6.93
% 6.55/6.93 *** allocated 256285 integers for clauses
% 6.55/6.93 Resimplifying inuse:
% 6.55/6.93 Done
% 6.55/6.93
% 6.55/6.93 *** allocated 113905 integers for termspace/termends
% 6.55/6.93
% 6.55/6.93 Intermediate Status:
% 6.55/6.93 Generated: 49413
% 6.55/6.93 Kept: 6075
% 6.55/6.93 Inuse: 560
% 6.55/6.93 Deleted: 6
% 6.55/6.93 Deletedinuse: 3
% 6.55/6.93
% 6.55/6.93 Resimplifying inuse:
% 6.55/6.93 Done
% 6.55/6.93
% 6.55/6.93 *** allocated 384427 integers for clauses
% 6.55/6.93 Resimplifying inuse:
% 6.55/6.93 Done
% 6.55/6.93
% 6.55/6.93 *** allocated 170857 integers for termspace/termends
% 6.55/6.93
% 6.55/6.93 Intermediate Status:
% 6.55/6.93 Generated: 81037
% 6.55/6.93 Kept: 8081
% 6.55/6.93 Inuse: 790
% 6.55/6.93 Deleted: 6
% 6.55/6.93 Deletedinuse: 3
% 6.55/6.93
% 6.55/6.93 Resimplifying inuse:
% 6.55/6.93 Done
% 6.55/6.93
% 6.55/6.93 *** allocated 576640 integers for clauses
% 6.55/6.93 Resimplifying inuse:
% 6.55/6.93 Done
% 6.55/6.93
% 6.55/6.93
% 6.55/6.93 Bliksems!, er is een bewijs:
% 6.55/6.93 % SZS status Theorem
% 6.55/6.93 % SZS output start Refutation
% 6.55/6.93
% 6.55/6.93 (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 6.55/6.93 (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 6.55/6.93 (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 6.55/6.93 (3) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ), distinct_points( Y, Z
% 6.55/6.93 ), ! distinct_points( X, Y ) }.
% 6.55/6.93 (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 6.55/6.93 , ! distinct_lines( X, Y ) }.
% 6.55/6.93 (8) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 6.55/6.93 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 6.55/6.93 (9) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 6.55/6.93 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 6.55/6.93 (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! distinct_lines(
% 6.55/6.93 Z, T ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 6.55/6.93 apart_point_and_line( Y, T ), apart_point_and_line( X, Z ) }.
% 6.55/6.93 (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ), convergent_lines(
% 6.55/6.93 X, Z ), distinct_lines( Y, Z ) }.
% 6.55/6.93 (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! distinct_lines( X
% 6.55/6.93 , Y ) }.
% 6.55/6.93 (37) {G0,W6,D2,L2,V2,M1} I { distinct_points( X, Y ), equal_points( X, Y )
% 6.55/6.93 }.
% 6.55/6.93 (42) {G0,W6,D2,L2,V2,M1} I { ! apart_point_and_line( X, Y ), !
% 6.55/6.93 incident_point_and_line( X, Y ) }.
% 6.55/6.93 (46) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 ) }.
% 6.55/6.93 (47) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol3, skol1 ) }.
% 6.55/6.93 (48) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol3, skol2 ) }.
% 6.55/6.93 (49) {G0,W5,D3,L1,V0,M1} I { ! equal_points( skol3, intersection_point(
% 6.55/6.93 skol1, skol2 ) ) }.
% 6.55/6.93 (52) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ),
% 6.55/6.93 distinct_points( X, Y ) }.
% 6.55/6.93 (55) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 6.55/6.93 ( X, Y ) }.
% 6.55/6.93 (56) {G2,W9,D2,L3,V3,M3} R(55,4) { distinct_lines( Z, X ), ! distinct_lines
% 6.55/6.93 ( Y, Z ), distinct_lines( X, Y ) }.
% 6.55/6.93 (73) {G1,W3,D2,L1,V0,M1} R(42,47) { ! apart_point_and_line( skol3, skol1 )
% 6.55/6.93 }.
% 6.55/6.93 (74) {G1,W3,D2,L1,V0,M1} R(42,48) { ! apart_point_and_line( skol3, skol2 )
% 6.55/6.93 }.
% 6.55/6.93 (75) {G1,W5,D3,L1,V0,M1} R(37,49) { distinct_points( skol3,
% 6.55/6.93 intersection_point( skol1, skol2 ) ) }.
% 6.55/6.93 (76) {G2,W5,D3,L1,V0,M1} R(75,52) { distinct_points( intersection_point(
% 6.55/6.93 skol1, skol2 ), skol3 ) }.
% 6.55/6.93 (78) {G1,W22,D3,L6,V4,M3} R(10,9) { ! distinct_points( intersection_point(
% 6.55/6.93 X, Y ), Z ), ! distinct_lines( T, Y ), ! convergent_lines( X, Y ),
% 6.55/6.93 apart_point_and_line( intersection_point( X, Y ), T ),
% 6.55/6.93 apart_point_and_line( Z, T ), apart_point_and_line( Z, Y ) }.
% 6.55/6.93 (129) {G2,W6,D2,L2,V2,M1} R(14,55) { convergent_lines( X, Y ), !
% 6.55/6.93 distinct_lines( Y, X ) }.
% 6.55/6.93 (492) {G3,W9,D2,L3,V3,M2} R(56,129) { convergent_lines( Z, Y ), !
% 6.55/6.93 distinct_lines( X, Y ), distinct_lines( Z, X ) }.
% 6.55/6.93 (505) {G4,W12,D2,L4,V4,M1} R(492,13) { convergent_lines( X, Y ), !
% 6.55/6.93 convergent_lines( T, Z ), convergent_lines( T, Y ), distinct_lines( X, Z
% 6.55/6.93 ) }.
% 6.55/6.93 (511) {G5,W9,D2,L3,V3,M1} F(505) { convergent_lines( X, Y ), !
% 6.55/6.93 convergent_lines( X, Z ), distinct_lines( X, Z ) }.
% 6.55/6.93 (516) {G6,W9,D2,L3,V3,M1} R(511,55) { convergent_lines( X, Y ), !
% 6.55/6.93 convergent_lines( X, Z ), distinct_lines( Z, X ) }.
% 6.55/6.93 (518) {G7,W12,D2,L4,V4,M1} R(516,492) { convergent_lines( X, Y ), !
% 6.55/6.93 convergent_lines( X, Z ), convergent_lines( T, X ), distinct_lines( T, Z
% 6.55/6.93 ) }.
% 6.55/6.93 (520) {G8,W6,D2,L2,V2,M1} F(518);r(2) { ! convergent_lines( X, Y ),
% 6.55/6.93 distinct_lines( X, Y ) }.
% 6.55/6.93 (914) {G9,W14,D3,L4,V3,M2} R(78,8);f;r(520) { ! convergent_lines( X, Y ), !
% 6.55/6.93 distinct_points( intersection_point( X, Y ), Z ), apart_point_and_line(
% 6.55/6.93 Z, Y ), apart_point_and_line( Z, X ) }.
% 6.55/6.93 (10038) {G10,W11,D3,L3,V1,M1} R(914,74) { ! convergent_lines( X, skol2 ), !
% 6.55/6.93 distinct_points( intersection_point( X, skol2 ), skol3 ),
% 6.55/6.93 apart_point_and_line( skol3, X ) }.
% 6.55/6.93 (10074) {G11,W5,D3,L1,V0,M1} R(10038,73);r(46) { ! distinct_points(
% 6.55/6.93 intersection_point( skol1, skol2 ), skol3 ) }.
% 6.55/6.93 (10079) {G12,W0,D0,L0,V0,M0} S(10074);r(76) { }.
% 6.55/6.93
% 6.55/6.93
% 6.55/6.93 % SZS output end Refutation
% 6.55/6.93 found a proof!
% 6.55/6.93
% 6.55/6.93
% 6.55/6.93 Unprocessed initial clauses:
% 6.55/6.93
% 6.55/6.93 (10081) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 6.55/6.93 (10082) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 6.55/6.93 (10083) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 6.55/6.93 (10084) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points(
% 6.55/6.93 X, Z ), distinct_points( Y, Z ) }.
% 6.55/6.93 (10085) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X
% 6.55/6.93 , Z ), distinct_lines( Y, Z ) }.
% 6.55/6.93 (10086) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines
% 6.55/6.93 ( X, Z ), convergent_lines( Y, Z ) }.
% 6.55/6.93 (10087) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 6.55/6.93 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 6.55/6.93 (10088) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 6.55/6.93 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 6.55/6.93 (10089) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 6.55/6.93 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 6.55/6.93 (10090) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 6.55/6.93 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 6.55/6.93 (10091) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines
% 6.55/6.93 ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 6.55/6.93 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 6.55/6.93 (10092) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 6.55/6.93 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 6.55/6.93 (10093) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 6.55/6.93 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 6.55/6.93 (10094) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), distinct_lines(
% 6.55/6.93 Y, Z ), convergent_lines( X, Z ) }.
% 6.55/6.93 (10095) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ), convergent_lines(
% 6.55/6.93 X, Y ) }.
% 6.55/6.93 (10096) {G0,W5,D3,L1,V2,M1} { ! convergent_lines( parallel_through_point(
% 6.55/6.93 Y, X ), Y ) }.
% 6.55/6.93 (10097) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 6.55/6.93 parallel_through_point( Y, X ) ) }.
% 6.55/6.93 (10098) {G0,W12,D2,L4,V3,M4} { ! distinct_lines( X, Y ),
% 6.55/6.93 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 6.55/6.93 convergent_lines( X, Y ) }.
% 6.55/6.93 (10099) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines
% 6.55/6.93 ( X, Y ) }.
% 6.55/6.93 (10100) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 6.55/6.93 unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 6.55/6.93 (10101) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 6.55/6.93 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 6.55/6.93 }.
% 6.55/6.93 (10102) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines( X, Y )
% 6.55/6.93 }.
% 6.55/6.93 (10103) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 6.55/6.93 }.
% 6.55/6.93 (10104) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( X, Y ), !
% 6.55/6.93 unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 6.55/6.93 (10105) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines(
% 6.55/6.93 orthogonal_through_point( Y, X ), Y ) }.
% 6.55/6.93 (10106) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 6.55/6.93 orthogonal_through_point( Y, X ) ) }.
% 6.55/6.93 (10107) {G0,W15,D2,L5,V4,M5} { ! distinct_lines( X, Y ),
% 6.55/6.93 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 6.55/6.93 unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 6.55/6.93 (10108) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines
% 6.55/6.93 ( X, Y ) }.
% 6.55/6.93 (10109) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), convergent_lines( Z, Y ), !
% 6.55/6.93 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 6.55/6.93 (10110) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), unorthogonal_lines( Z, Y )
% 6.55/6.93 , ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 6.55/6.93 (10111) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), convergent_lines( Y, X )
% 6.55/6.93 }.
% 6.55/6.93 (10112) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), unorthogonal_lines( Y, X )
% 6.55/6.93 }.
% 6.55/6.93 (10113) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( Y, X ), !
% 6.55/6.93 unorthogonal_lines( Y, X ), alpha2( X, Y ) }.
% 6.55/6.93 (10114) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ),
% 6.55/6.93 unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 6.55/6.93 (10115) {G0,W11,D3,L4,V2,M4} { ! point( X ), ! point( Y ), !
% 6.55/6.93 distinct_points( X, Y ), line( line_connecting( X, Y ) ) }.
% 6.55/6.93 (10116) {G0,W11,D3,L4,V2,M4} { ! line( X ), ! line( Y ), !
% 6.55/6.93 convergent_lines( X, Y ), point( intersection_point( X, Y ) ) }.
% 6.55/6.93 (10117) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 6.55/6.93 parallel_through_point( X, Y ) ) }.
% 6.55/6.93 (10118) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 6.55/6.93 orthogonal_through_point( X, Y ) ) }.
% 6.55/6.93 (10119) {G0,W6,D2,L2,V2,M2} { ! equal_points( X, Y ), ! distinct_points( X
% 6.55/6.93 , Y ) }.
% 6.55/6.93 (10120) {G0,W6,D2,L2,V2,M2} { distinct_points( X, Y ), equal_points( X, Y
% 6.55/6.93 ) }.
% 6.55/6.93 (10121) {G0,W6,D2,L2,V2,M2} { ! equal_lines( X, Y ), ! distinct_lines( X,
% 6.55/6.93 Y ) }.
% 6.55/6.93 (10122) {G0,W6,D2,L2,V2,M2} { distinct_lines( X, Y ), equal_lines( X, Y )
% 6.55/6.93 }.
% 6.55/6.93 (10123) {G0,W6,D2,L2,V2,M2} { ! parallel_lines( X, Y ), ! convergent_lines
% 6.55/6.93 ( X, Y ) }.
% 6.55/6.93 (10124) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), parallel_lines( X
% 6.55/6.93 , Y ) }.
% 6.55/6.93 (10125) {G0,W6,D2,L2,V2,M2} { ! incident_point_and_line( X, Y ), !
% 6.55/6.93 apart_point_and_line( X, Y ) }.
% 6.55/6.93 (10126) {G0,W6,D2,L2,V2,M2} { apart_point_and_line( X, Y ),
% 6.55/6.93 incident_point_and_line( X, Y ) }.
% 6.55/6.93 (10127) {G0,W6,D2,L2,V2,M2} { ! orthogonal_lines( X, Y ), !
% 6.55/6.93 unorthogonal_lines( X, Y ) }.
% 6.55/6.93 (10128) {G0,W6,D2,L2,V2,M2} { unorthogonal_lines( X, Y ), orthogonal_lines
% 6.55/6.93 ( X, Y ) }.
% 6.55/6.93 (10129) {G0,W3,D2,L1,V0,M1} { convergent_lines( skol1, skol2 ) }.
% 6.55/6.93 (10130) {G0,W3,D2,L1,V0,M1} { incident_point_and_line( skol3, skol1 ) }.
% 6.55/6.93 (10131) {G0,W3,D2,L1,V0,M1} { incident_point_and_line( skol3, skol2 ) }.
% 6.55/6.93 (10132) {G0,W5,D3,L1,V0,M1} { ! equal_points( skol3, intersection_point(
% 6.55/6.93 skol1, skol2 ) ) }.
% 6.55/6.93
% 6.55/6.93
% 6.55/6.93 Total Proof:
% 6.55/6.93
% 6.55/6.93 subsumption: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 6.55/6.93 parent0: (10081) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := X
% 6.55/6.93 end
% 6.55/6.93 permutation0:
% 6.55/6.93 0 ==> 0
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 6.55/6.93 parent0: (10082) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := X
% 6.55/6.93 end
% 6.55/6.93 permutation0:
% 6.55/6.93 0 ==> 0
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 subsumption: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 6.55/6.93 parent0: (10083) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := X
% 6.55/6.93 end
% 6.55/6.93 permutation0:
% 6.55/6.93 0 ==> 0
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 subsumption: (3) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ),
% 6.55/6.93 distinct_points( Y, Z ), ! distinct_points( X, Y ) }.
% 6.55/6.93 parent0: (10084) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ),
% 6.55/6.93 distinct_points( X, Z ), distinct_points( Y, Z ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := X
% 6.55/6.93 Y := Y
% 6.55/6.93 Z := Z
% 6.55/6.93 end
% 6.55/6.93 permutation0:
% 6.55/6.93 0 ==> 2
% 6.55/6.93 1 ==> 0
% 6.55/6.93 2 ==> 1
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 6.55/6.93 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 6.55/6.93 parent0: (10085) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ),
% 6.55/6.93 distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := X
% 6.55/6.93 Y := Y
% 6.55/6.93 Z := Z
% 6.55/6.93 end
% 6.55/6.93 permutation0:
% 6.55/6.93 0 ==> 2
% 6.55/6.93 1 ==> 0
% 6.55/6.93 2 ==> 1
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 subsumption: (8) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 6.55/6.93 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 6.55/6.93 parent0: (10089) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 6.55/6.93 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := X
% 6.55/6.93 Y := Y
% 6.55/6.93 end
% 6.55/6.93 permutation0:
% 6.55/6.93 0 ==> 0
% 6.55/6.93 1 ==> 1
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 subsumption: (9) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 6.55/6.93 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 6.55/6.93 parent0: (10090) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 6.55/6.93 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := X
% 6.55/6.93 Y := Y
% 6.55/6.93 end
% 6.55/6.93 permutation0:
% 6.55/6.93 0 ==> 0
% 6.55/6.93 1 ==> 1
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 subsumption: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), !
% 6.55/6.93 distinct_lines( Z, T ), apart_point_and_line( X, T ),
% 6.55/6.93 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ),
% 6.55/6.93 apart_point_and_line( X, Z ) }.
% 6.55/6.93 parent0: (10091) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), !
% 6.55/6.93 distinct_lines( Z, T ), apart_point_and_line( X, Z ),
% 6.55/6.93 apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 6.55/6.93 apart_point_and_line( Y, T ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := X
% 6.55/6.93 Y := Y
% 6.55/6.93 Z := Z
% 6.55/6.93 T := T
% 6.55/6.93 end
% 6.55/6.93 permutation0:
% 6.55/6.93 0 ==> 0
% 6.55/6.93 1 ==> 1
% 6.55/6.93 2 ==> 5
% 6.55/6.93 3 ==> 2
% 6.55/6.93 4 ==> 3
% 6.55/6.93 5 ==> 4
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 subsumption: (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ),
% 6.55/6.93 convergent_lines( X, Z ), distinct_lines( Y, Z ) }.
% 6.55/6.93 parent0: (10094) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 6.55/6.93 distinct_lines( Y, Z ), convergent_lines( X, Z ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := X
% 6.55/6.93 Y := Y
% 6.55/6.93 Z := Z
% 6.55/6.93 end
% 6.55/6.93 permutation0:
% 6.55/6.93 0 ==> 0
% 6.55/6.93 1 ==> 2
% 6.55/6.93 2 ==> 1
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 subsumption: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 6.55/6.93 distinct_lines( X, Y ) }.
% 6.55/6.93 parent0: (10095) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ),
% 6.55/6.93 convergent_lines( X, Y ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := X
% 6.55/6.93 Y := Y
% 6.55/6.93 end
% 6.55/6.93 permutation0:
% 6.55/6.93 0 ==> 1
% 6.55/6.93 1 ==> 0
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 subsumption: (37) {G0,W6,D2,L2,V2,M1} I { distinct_points( X, Y ),
% 6.55/6.93 equal_points( X, Y ) }.
% 6.55/6.93 parent0: (10120) {G0,W6,D2,L2,V2,M2} { distinct_points( X, Y ),
% 6.55/6.93 equal_points( X, Y ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := X
% 6.55/6.93 Y := Y
% 6.55/6.93 end
% 6.55/6.93 permutation0:
% 6.55/6.93 0 ==> 0
% 6.55/6.93 1 ==> 1
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 subsumption: (42) {G0,W6,D2,L2,V2,M1} I { ! apart_point_and_line( X, Y ), !
% 6.55/6.93 incident_point_and_line( X, Y ) }.
% 6.55/6.93 parent0: (10125) {G0,W6,D2,L2,V2,M2} { ! incident_point_and_line( X, Y ),
% 6.55/6.93 ! apart_point_and_line( X, Y ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := X
% 6.55/6.93 Y := Y
% 6.55/6.93 end
% 6.55/6.93 permutation0:
% 6.55/6.93 0 ==> 1
% 6.55/6.93 1 ==> 0
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 subsumption: (46) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 )
% 6.55/6.93 }.
% 6.55/6.93 parent0: (10129) {G0,W3,D2,L1,V0,M1} { convergent_lines( skol1, skol2 )
% 6.55/6.93 }.
% 6.55/6.93 substitution0:
% 6.55/6.93 end
% 6.55/6.93 permutation0:
% 6.55/6.93 0 ==> 0
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 subsumption: (47) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol3,
% 6.55/6.93 skol1 ) }.
% 6.55/6.93 parent0: (10130) {G0,W3,D2,L1,V0,M1} { incident_point_and_line( skol3,
% 6.55/6.93 skol1 ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 end
% 6.55/6.93 permutation0:
% 6.55/6.93 0 ==> 0
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 subsumption: (48) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol3,
% 6.55/6.93 skol2 ) }.
% 6.55/6.93 parent0: (10131) {G0,W3,D2,L1,V0,M1} { incident_point_and_line( skol3,
% 6.55/6.93 skol2 ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 end
% 6.55/6.93 permutation0:
% 6.55/6.93 0 ==> 0
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 subsumption: (49) {G0,W5,D3,L1,V0,M1} I { ! equal_points( skol3,
% 6.55/6.93 intersection_point( skol1, skol2 ) ) }.
% 6.55/6.93 parent0: (10132) {G0,W5,D3,L1,V0,M1} { ! equal_points( skol3,
% 6.55/6.93 intersection_point( skol1, skol2 ) ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 end
% 6.55/6.93 permutation0:
% 6.55/6.93 0 ==> 0
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 resolution: (10259) {G1,W6,D2,L2,V2,M2} { distinct_points( Y, X ), !
% 6.55/6.93 distinct_points( X, Y ) }.
% 6.55/6.93 parent0[0]: (0) {G0,W3,D2,L1,V1,M1} I { ! distinct_points( X, X ) }.
% 6.55/6.93 parent1[0]: (3) {G0,W9,D2,L3,V3,M3} I { distinct_points( X, Z ),
% 6.55/6.93 distinct_points( Y, Z ), ! distinct_points( X, Y ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := X
% 6.55/6.93 end
% 6.55/6.93 substitution1:
% 6.55/6.93 X := X
% 6.55/6.93 Y := Y
% 6.55/6.93 Z := X
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 subsumption: (52) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ),
% 6.55/6.93 distinct_points( X, Y ) }.
% 6.55/6.93 parent0: (10259) {G1,W6,D2,L2,V2,M2} { distinct_points( Y, X ), !
% 6.55/6.93 distinct_points( X, Y ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := Y
% 6.55/6.93 Y := X
% 6.55/6.93 end
% 6.55/6.93 permutation0:
% 6.55/6.93 0 ==> 1
% 6.55/6.93 1 ==> 0
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 resolution: (10261) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 6.55/6.93 distinct_lines( X, Y ) }.
% 6.55/6.93 parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 6.55/6.93 parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 6.55/6.93 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := X
% 6.55/6.93 end
% 6.55/6.93 substitution1:
% 6.55/6.93 X := X
% 6.55/6.93 Y := Y
% 6.55/6.93 Z := X
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 subsumption: (55) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 6.55/6.93 distinct_lines( X, Y ) }.
% 6.55/6.93 parent0: (10261) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 6.55/6.93 distinct_lines( X, Y ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := Y
% 6.55/6.93 Y := X
% 6.55/6.93 end
% 6.55/6.93 permutation0:
% 6.55/6.93 0 ==> 1
% 6.55/6.93 1 ==> 0
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 resolution: (10263) {G1,W9,D2,L3,V3,M3} { distinct_lines( Y, X ),
% 6.55/6.93 distinct_lines( Z, Y ), ! distinct_lines( X, Z ) }.
% 6.55/6.93 parent0[0]: (55) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 6.55/6.93 distinct_lines( X, Y ) }.
% 6.55/6.93 parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 6.55/6.93 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := Y
% 6.55/6.93 Y := X
% 6.55/6.93 end
% 6.55/6.93 substitution1:
% 6.55/6.93 X := X
% 6.55/6.93 Y := Z
% 6.55/6.93 Z := Y
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 subsumption: (56) {G2,W9,D2,L3,V3,M3} R(55,4) { distinct_lines( Z, X ), !
% 6.55/6.93 distinct_lines( Y, Z ), distinct_lines( X, Y ) }.
% 6.55/6.93 parent0: (10263) {G1,W9,D2,L3,V3,M3} { distinct_lines( Y, X ),
% 6.55/6.93 distinct_lines( Z, Y ), ! distinct_lines( X, Z ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := Y
% 6.55/6.93 Y := X
% 6.55/6.93 Z := Z
% 6.55/6.93 end
% 6.55/6.93 permutation0:
% 6.55/6.93 0 ==> 2
% 6.55/6.93 1 ==> 0
% 6.55/6.93 2 ==> 1
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 resolution: (10266) {G1,W3,D2,L1,V0,M1} { ! apart_point_and_line( skol3,
% 6.55/6.93 skol1 ) }.
% 6.55/6.93 parent0[1]: (42) {G0,W6,D2,L2,V2,M1} I { ! apart_point_and_line( X, Y ), !
% 6.55/6.93 incident_point_and_line( X, Y ) }.
% 6.55/6.93 parent1[0]: (47) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol3,
% 6.55/6.93 skol1 ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := skol3
% 6.55/6.93 Y := skol1
% 6.55/6.93 end
% 6.55/6.93 substitution1:
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 subsumption: (73) {G1,W3,D2,L1,V0,M1} R(42,47) { ! apart_point_and_line(
% 6.55/6.93 skol3, skol1 ) }.
% 6.55/6.93 parent0: (10266) {G1,W3,D2,L1,V0,M1} { ! apart_point_and_line( skol3,
% 6.55/6.93 skol1 ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 end
% 6.55/6.93 permutation0:
% 6.55/6.93 0 ==> 0
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 resolution: (10267) {G1,W3,D2,L1,V0,M1} { ! apart_point_and_line( skol3,
% 6.55/6.93 skol2 ) }.
% 6.55/6.93 parent0[1]: (42) {G0,W6,D2,L2,V2,M1} I { ! apart_point_and_line( X, Y ), !
% 6.55/6.93 incident_point_and_line( X, Y ) }.
% 6.55/6.93 parent1[0]: (48) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol3,
% 6.55/6.93 skol2 ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := skol3
% 6.55/6.93 Y := skol2
% 6.55/6.93 end
% 6.55/6.93 substitution1:
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 subsumption: (74) {G1,W3,D2,L1,V0,M1} R(42,48) { ! apart_point_and_line(
% 6.55/6.93 skol3, skol2 ) }.
% 6.55/6.93 parent0: (10267) {G1,W3,D2,L1,V0,M1} { ! apart_point_and_line( skol3,
% 6.55/6.93 skol2 ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 end
% 6.55/6.93 permutation0:
% 6.55/6.93 0 ==> 0
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 resolution: (10268) {G1,W5,D3,L1,V0,M1} { distinct_points( skol3,
% 6.55/6.93 intersection_point( skol1, skol2 ) ) }.
% 6.55/6.93 parent0[0]: (49) {G0,W5,D3,L1,V0,M1} I { ! equal_points( skol3,
% 6.55/6.93 intersection_point( skol1, skol2 ) ) }.
% 6.55/6.93 parent1[1]: (37) {G0,W6,D2,L2,V2,M1} I { distinct_points( X, Y ),
% 6.55/6.93 equal_points( X, Y ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 end
% 6.55/6.93 substitution1:
% 6.55/6.93 X := skol3
% 6.55/6.93 Y := intersection_point( skol1, skol2 )
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 subsumption: (75) {G1,W5,D3,L1,V0,M1} R(37,49) { distinct_points( skol3,
% 6.55/6.93 intersection_point( skol1, skol2 ) ) }.
% 6.55/6.93 parent0: (10268) {G1,W5,D3,L1,V0,M1} { distinct_points( skol3,
% 6.55/6.93 intersection_point( skol1, skol2 ) ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 end
% 6.55/6.93 permutation0:
% 6.55/6.93 0 ==> 0
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 resolution: (10269) {G2,W5,D3,L1,V0,M1} { distinct_points(
% 6.55/6.93 intersection_point( skol1, skol2 ), skol3 ) }.
% 6.55/6.93 parent0[0]: (52) {G1,W6,D2,L2,V2,M2} R(3,0) { ! distinct_points( Y, X ),
% 6.55/6.93 distinct_points( X, Y ) }.
% 6.55/6.93 parent1[0]: (75) {G1,W5,D3,L1,V0,M1} R(37,49) { distinct_points( skol3,
% 6.55/6.93 intersection_point( skol1, skol2 ) ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := intersection_point( skol1, skol2 )
% 6.55/6.93 Y := skol3
% 6.55/6.93 end
% 6.55/6.93 substitution1:
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 subsumption: (76) {G2,W5,D3,L1,V0,M1} R(75,52) { distinct_points(
% 6.55/6.93 intersection_point( skol1, skol2 ), skol3 ) }.
% 6.55/6.93 parent0: (10269) {G2,W5,D3,L1,V0,M1} { distinct_points( intersection_point
% 6.55/6.93 ( skol1, skol2 ), skol3 ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 end
% 6.55/6.93 permutation0:
% 6.55/6.93 0 ==> 0
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 resolution: (10270) {G1,W22,D3,L6,V4,M6} { ! convergent_lines( X, Y ), !
% 6.55/6.93 distinct_points( intersection_point( X, Y ), Z ), ! distinct_lines( T, Y
% 6.55/6.93 ), apart_point_and_line( Z, T ), apart_point_and_line( Z, Y ),
% 6.55/6.93 apart_point_and_line( intersection_point( X, Y ), T ) }.
% 6.55/6.93 parent0[1]: (9) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 6.55/6.93 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 6.55/6.93 parent1[2]: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), !
% 6.55/6.93 distinct_lines( Z, T ), apart_point_and_line( X, T ),
% 6.55/6.93 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ),
% 6.55/6.93 apart_point_and_line( X, Z ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := X
% 6.55/6.93 Y := Y
% 6.55/6.93 end
% 6.55/6.93 substitution1:
% 6.55/6.93 X := intersection_point( X, Y )
% 6.55/6.93 Y := Z
% 6.55/6.93 Z := T
% 6.55/6.93 T := Y
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 subsumption: (78) {G1,W22,D3,L6,V4,M3} R(10,9) { ! distinct_points(
% 6.55/6.93 intersection_point( X, Y ), Z ), ! distinct_lines( T, Y ), !
% 6.55/6.93 convergent_lines( X, Y ), apart_point_and_line( intersection_point( X, Y
% 6.55/6.93 ), T ), apart_point_and_line( Z, T ), apart_point_and_line( Z, Y ) }.
% 6.55/6.93 parent0: (10270) {G1,W22,D3,L6,V4,M6} { ! convergent_lines( X, Y ), !
% 6.55/6.93 distinct_points( intersection_point( X, Y ), Z ), ! distinct_lines( T, Y
% 6.55/6.93 ), apart_point_and_line( Z, T ), apart_point_and_line( Z, Y ),
% 6.55/6.93 apart_point_and_line( intersection_point( X, Y ), T ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := X
% 6.55/6.93 Y := Y
% 6.55/6.93 Z := Z
% 6.55/6.93 T := T
% 6.55/6.93 end
% 6.55/6.93 permutation0:
% 6.55/6.93 0 ==> 2
% 6.55/6.93 1 ==> 0
% 6.55/6.93 2 ==> 1
% 6.55/6.93 3 ==> 4
% 6.55/6.93 4 ==> 5
% 6.55/6.93 5 ==> 3
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 resolution: (10279) {G1,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), !
% 6.55/6.93 distinct_lines( Y, X ) }.
% 6.55/6.93 parent0[1]: (14) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 6.55/6.93 distinct_lines( X, Y ) }.
% 6.55/6.93 parent1[1]: (55) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 6.55/6.93 distinct_lines( X, Y ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := X
% 6.55/6.93 Y := Y
% 6.55/6.93 end
% 6.55/6.93 substitution1:
% 6.55/6.93 X := X
% 6.55/6.93 Y := Y
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 subsumption: (129) {G2,W6,D2,L2,V2,M1} R(14,55) { convergent_lines( X, Y )
% 6.55/6.93 , ! distinct_lines( Y, X ) }.
% 6.55/6.93 parent0: (10279) {G1,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), !
% 6.55/6.93 distinct_lines( Y, X ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := X
% 6.55/6.93 Y := Y
% 6.55/6.93 end
% 6.55/6.93 permutation0:
% 6.55/6.93 0 ==> 0
% 6.55/6.93 1 ==> 1
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 resolution: (10280) {G3,W9,D2,L3,V3,M3} { convergent_lines( X, Y ), !
% 6.55/6.93 distinct_lines( Z, Y ), distinct_lines( X, Z ) }.
% 6.55/6.93 parent0[1]: (129) {G2,W6,D2,L2,V2,M1} R(14,55) { convergent_lines( X, Y ),
% 6.55/6.93 ! distinct_lines( Y, X ) }.
% 6.55/6.93 parent1[0]: (56) {G2,W9,D2,L3,V3,M3} R(55,4) { distinct_lines( Z, X ), !
% 6.55/6.93 distinct_lines( Y, Z ), distinct_lines( X, Y ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := X
% 6.55/6.93 Y := Y
% 6.55/6.93 end
% 6.55/6.93 substitution1:
% 6.55/6.93 X := X
% 6.55/6.93 Y := Z
% 6.55/6.93 Z := Y
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 subsumption: (492) {G3,W9,D2,L3,V3,M2} R(56,129) { convergent_lines( Z, Y )
% 6.55/6.93 , ! distinct_lines( X, Y ), distinct_lines( Z, X ) }.
% 6.55/6.93 parent0: (10280) {G3,W9,D2,L3,V3,M3} { convergent_lines( X, Y ), !
% 6.55/6.93 distinct_lines( Z, Y ), distinct_lines( X, Z ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := Z
% 6.55/6.93 Y := Y
% 6.55/6.93 Z := X
% 6.55/6.93 end
% 6.55/6.93 permutation0:
% 6.55/6.93 0 ==> 0
% 6.55/6.93 1 ==> 1
% 6.55/6.93 2 ==> 2
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 resolution: (10282) {G1,W12,D2,L4,V4,M4} { convergent_lines( X, Y ),
% 6.55/6.93 distinct_lines( X, Z ), ! convergent_lines( T, Z ), convergent_lines( T,
% 6.55/6.93 Y ) }.
% 6.55/6.93 parent0[1]: (492) {G3,W9,D2,L3,V3,M2} R(56,129) { convergent_lines( Z, Y )
% 6.55/6.93 , ! distinct_lines( X, Y ), distinct_lines( Z, X ) }.
% 6.55/6.93 parent1[2]: (13) {G0,W9,D2,L3,V3,M1} I { ! convergent_lines( X, Y ),
% 6.55/6.93 convergent_lines( X, Z ), distinct_lines( Y, Z ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := Z
% 6.55/6.93 Y := Y
% 6.55/6.93 Z := X
% 6.55/6.93 end
% 6.55/6.93 substitution1:
% 6.55/6.93 X := T
% 6.55/6.93 Y := Z
% 6.55/6.93 Z := Y
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 subsumption: (505) {G4,W12,D2,L4,V4,M1} R(492,13) { convergent_lines( X, Y
% 6.55/6.93 ), ! convergent_lines( T, Z ), convergent_lines( T, Y ), distinct_lines
% 6.55/6.93 ( X, Z ) }.
% 6.55/6.93 parent0: (10282) {G1,W12,D2,L4,V4,M4} { convergent_lines( X, Y ),
% 6.55/6.93 distinct_lines( X, Z ), ! convergent_lines( T, Z ), convergent_lines( T,
% 6.55/6.93 Y ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := X
% 6.55/6.93 Y := Y
% 6.55/6.93 Z := Z
% 6.55/6.93 T := T
% 6.55/6.93 end
% 6.55/6.93 permutation0:
% 6.55/6.93 0 ==> 0
% 6.55/6.93 1 ==> 3
% 6.55/6.93 2 ==> 1
% 6.55/6.93 3 ==> 2
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 factor: (10284) {G4,W9,D2,L3,V3,M3} { convergent_lines( X, Y ), !
% 6.55/6.93 convergent_lines( X, Z ), distinct_lines( X, Z ) }.
% 6.55/6.93 parent0[0, 2]: (505) {G4,W12,D2,L4,V4,M1} R(492,13) { convergent_lines( X,
% 6.55/6.93 Y ), ! convergent_lines( T, Z ), convergent_lines( T, Y ), distinct_lines
% 6.55/6.93 ( X, Z ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := X
% 6.55/6.93 Y := Y
% 6.55/6.93 Z := Z
% 6.55/6.93 T := X
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 subsumption: (511) {G5,W9,D2,L3,V3,M1} F(505) { convergent_lines( X, Y ), !
% 6.55/6.93 convergent_lines( X, Z ), distinct_lines( X, Z ) }.
% 6.55/6.93 parent0: (10284) {G4,W9,D2,L3,V3,M3} { convergent_lines( X, Y ), !
% 6.55/6.93 convergent_lines( X, Z ), distinct_lines( X, Z ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := X
% 6.55/6.93 Y := Y
% 6.55/6.93 Z := Z
% 6.55/6.93 end
% 6.55/6.93 permutation0:
% 6.55/6.93 0 ==> 0
% 6.55/6.93 1 ==> 1
% 6.55/6.93 2 ==> 2
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 resolution: (10285) {G2,W9,D2,L3,V3,M3} { distinct_lines( Y, X ),
% 6.55/6.93 convergent_lines( X, Z ), ! convergent_lines( X, Y ) }.
% 6.55/6.93 parent0[0]: (55) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 6.55/6.93 distinct_lines( X, Y ) }.
% 6.55/6.93 parent1[2]: (511) {G5,W9,D2,L3,V3,M1} F(505) { convergent_lines( X, Y ), !
% 6.55/6.93 convergent_lines( X, Z ), distinct_lines( X, Z ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := Y
% 6.55/6.93 Y := X
% 6.55/6.93 end
% 6.55/6.93 substitution1:
% 6.55/6.93 X := X
% 6.55/6.93 Y := Z
% 6.55/6.93 Z := Y
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 subsumption: (516) {G6,W9,D2,L3,V3,M1} R(511,55) { convergent_lines( X, Y )
% 6.55/6.93 , ! convergent_lines( X, Z ), distinct_lines( Z, X ) }.
% 6.55/6.93 parent0: (10285) {G2,W9,D2,L3,V3,M3} { distinct_lines( Y, X ),
% 6.55/6.93 convergent_lines( X, Z ), ! convergent_lines( X, Y ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := X
% 6.55/6.93 Y := Z
% 6.55/6.93 Z := Y
% 6.55/6.93 end
% 6.55/6.93 permutation0:
% 6.55/6.93 0 ==> 2
% 6.55/6.93 1 ==> 0
% 6.55/6.93 2 ==> 1
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 resolution: (10288) {G4,W12,D2,L4,V4,M4} { convergent_lines( X, Y ),
% 6.55/6.93 distinct_lines( X, Z ), convergent_lines( Y, T ), ! convergent_lines( Y,
% 6.55/6.93 Z ) }.
% 6.55/6.93 parent0[1]: (492) {G3,W9,D2,L3,V3,M2} R(56,129) { convergent_lines( Z, Y )
% 6.55/6.93 , ! distinct_lines( X, Y ), distinct_lines( Z, X ) }.
% 6.55/6.93 parent1[2]: (516) {G6,W9,D2,L3,V3,M1} R(511,55) { convergent_lines( X, Y )
% 6.55/6.93 , ! convergent_lines( X, Z ), distinct_lines( Z, X ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := Z
% 6.55/6.93 Y := Y
% 6.55/6.93 Z := X
% 6.55/6.93 end
% 6.55/6.93 substitution1:
% 6.55/6.93 X := Y
% 6.55/6.93 Y := T
% 6.55/6.93 Z := Z
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 subsumption: (518) {G7,W12,D2,L4,V4,M1} R(516,492) { convergent_lines( X, Y
% 6.55/6.93 ), ! convergent_lines( X, Z ), convergent_lines( T, X ), distinct_lines
% 6.55/6.93 ( T, Z ) }.
% 6.55/6.93 parent0: (10288) {G4,W12,D2,L4,V4,M4} { convergent_lines( X, Y ),
% 6.55/6.93 distinct_lines( X, Z ), convergent_lines( Y, T ), ! convergent_lines( Y,
% 6.55/6.93 Z ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := T
% 6.55/6.93 Y := X
% 6.55/6.93 Z := Z
% 6.55/6.93 T := Y
% 6.55/6.93 end
% 6.55/6.93 permutation0:
% 6.55/6.93 0 ==> 2
% 6.55/6.93 1 ==> 3
% 6.55/6.93 2 ==> 0
% 6.55/6.93 3 ==> 1
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 factor: (10290) {G7,W9,D2,L3,V2,M3} { convergent_lines( X, X ), !
% 6.55/6.93 convergent_lines( X, Y ), distinct_lines( X, Y ) }.
% 6.55/6.93 parent0[0, 2]: (518) {G7,W12,D2,L4,V4,M1} R(516,492) { convergent_lines( X
% 6.55/6.93 , Y ), ! convergent_lines( X, Z ), convergent_lines( T, X ),
% 6.55/6.93 distinct_lines( T, Z ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := X
% 6.55/6.93 Y := X
% 6.55/6.93 Z := Y
% 6.55/6.93 T := X
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 resolution: (10291) {G1,W6,D2,L2,V2,M2} { ! convergent_lines( X, Y ),
% 6.55/6.93 distinct_lines( X, Y ) }.
% 6.55/6.93 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 6.55/6.93 parent1[0]: (10290) {G7,W9,D2,L3,V2,M3} { convergent_lines( X, X ), !
% 6.55/6.93 convergent_lines( X, Y ), distinct_lines( X, Y ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := X
% 6.55/6.93 end
% 6.55/6.93 substitution1:
% 6.55/6.93 X := X
% 6.55/6.93 Y := Y
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 subsumption: (520) {G8,W6,D2,L2,V2,M1} F(518);r(2) { ! convergent_lines( X
% 6.55/6.93 , Y ), distinct_lines( X, Y ) }.
% 6.55/6.93 parent0: (10291) {G1,W6,D2,L2,V2,M2} { ! convergent_lines( X, Y ),
% 6.55/6.93 distinct_lines( X, Y ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := X
% 6.55/6.93 Y := Y
% 6.55/6.93 end
% 6.55/6.93 permutation0:
% 6.55/6.93 0 ==> 0
% 6.55/6.93 1 ==> 1
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 resolution: (10292) {G1,W20,D3,L6,V3,M6} { ! convergent_lines( X, Y ), !
% 6.55/6.93 distinct_points( intersection_point( X, Y ), Z ), ! distinct_lines( X, Y
% 6.55/6.93 ), ! convergent_lines( X, Y ), apart_point_and_line( Z, X ),
% 6.55/6.93 apart_point_and_line( Z, Y ) }.
% 6.55/6.93 parent0[1]: (8) {G0,W8,D3,L2,V2,M1} I { ! convergent_lines( X, Y ), !
% 6.55/6.93 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 6.55/6.93 parent1[3]: (78) {G1,W22,D3,L6,V4,M3} R(10,9) { ! distinct_points(
% 6.55/6.93 intersection_point( X, Y ), Z ), ! distinct_lines( T, Y ), !
% 6.55/6.93 convergent_lines( X, Y ), apart_point_and_line( intersection_point( X, Y
% 6.55/6.93 ), T ), apart_point_and_line( Z, T ), apart_point_and_line( Z, Y ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := X
% 6.55/6.93 Y := Y
% 6.55/6.93 end
% 6.55/6.93 substitution1:
% 6.55/6.93 X := X
% 6.55/6.93 Y := Y
% 6.55/6.93 Z := Z
% 6.55/6.93 T := X
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 resolution: (10329) {G2,W20,D3,L6,V3,M6} { ! convergent_lines( X, Y ), !
% 6.55/6.93 distinct_points( intersection_point( X, Y ), Z ), ! convergent_lines( X,
% 6.55/6.93 Y ), apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), !
% 6.55/6.93 convergent_lines( X, Y ) }.
% 6.55/6.93 parent0[2]: (10292) {G1,W20,D3,L6,V3,M6} { ! convergent_lines( X, Y ), !
% 6.55/6.93 distinct_points( intersection_point( X, Y ), Z ), ! distinct_lines( X, Y
% 6.55/6.93 ), ! convergent_lines( X, Y ), apart_point_and_line( Z, X ),
% 6.55/6.93 apart_point_and_line( Z, Y ) }.
% 6.55/6.93 parent1[1]: (520) {G8,W6,D2,L2,V2,M1} F(518);r(2) { ! convergent_lines( X,
% 6.55/6.93 Y ), distinct_lines( X, Y ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := X
% 6.55/6.93 Y := Y
% 6.55/6.93 Z := Z
% 6.55/6.93 end
% 6.55/6.93 substitution1:
% 6.55/6.93 X := X
% 6.55/6.93 Y := Y
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 factor: (10330) {G2,W17,D3,L5,V3,M5} { ! convergent_lines( X, Y ), !
% 6.55/6.93 distinct_points( intersection_point( X, Y ), Z ), apart_point_and_line( Z
% 6.55/6.93 , X ), apart_point_and_line( Z, Y ), ! convergent_lines( X, Y ) }.
% 6.55/6.93 parent0[0, 2]: (10329) {G2,W20,D3,L6,V3,M6} { ! convergent_lines( X, Y ),
% 6.55/6.93 ! distinct_points( intersection_point( X, Y ), Z ), ! convergent_lines( X
% 6.55/6.93 , Y ), apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ), !
% 6.55/6.93 convergent_lines( X, Y ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := X
% 6.55/6.93 Y := Y
% 6.55/6.93 Z := Z
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 factor: (10331) {G2,W14,D3,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 6.55/6.93 distinct_points( intersection_point( X, Y ), Z ), apart_point_and_line( Z
% 6.55/6.93 , X ), apart_point_and_line( Z, Y ) }.
% 6.55/6.93 parent0[0, 4]: (10330) {G2,W17,D3,L5,V3,M5} { ! convergent_lines( X, Y ),
% 6.55/6.93 ! distinct_points( intersection_point( X, Y ), Z ), apart_point_and_line
% 6.55/6.93 ( Z, X ), apart_point_and_line( Z, Y ), ! convergent_lines( X, Y ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := X
% 6.55/6.93 Y := Y
% 6.55/6.93 Z := Z
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 subsumption: (914) {G9,W14,D3,L4,V3,M2} R(78,8);f;r(520) { !
% 6.55/6.93 convergent_lines( X, Y ), ! distinct_points( intersection_point( X, Y ),
% 6.55/6.93 Z ), apart_point_and_line( Z, Y ), apart_point_and_line( Z, X ) }.
% 6.55/6.93 parent0: (10331) {G2,W14,D3,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 6.55/6.93 distinct_points( intersection_point( X, Y ), Z ), apart_point_and_line( Z
% 6.55/6.93 , X ), apart_point_and_line( Z, Y ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := X
% 6.55/6.93 Y := Y
% 6.55/6.93 Z := Z
% 6.55/6.93 end
% 6.55/6.93 permutation0:
% 6.55/6.93 0 ==> 0
% 6.55/6.93 1 ==> 1
% 6.55/6.93 2 ==> 3
% 6.55/6.93 3 ==> 2
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 resolution: (10333) {G2,W11,D3,L3,V1,M3} { ! convergent_lines( X, skol2 )
% 6.55/6.93 , ! distinct_points( intersection_point( X, skol2 ), skol3 ),
% 6.55/6.93 apart_point_and_line( skol3, X ) }.
% 6.55/6.93 parent0[0]: (74) {G1,W3,D2,L1,V0,M1} R(42,48) { ! apart_point_and_line(
% 6.55/6.93 skol3, skol2 ) }.
% 6.55/6.93 parent1[2]: (914) {G9,W14,D3,L4,V3,M2} R(78,8);f;r(520) { !
% 6.55/6.93 convergent_lines( X, Y ), ! distinct_points( intersection_point( X, Y ),
% 6.55/6.93 Z ), apart_point_and_line( Z, Y ), apart_point_and_line( Z, X ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 end
% 6.55/6.93 substitution1:
% 6.55/6.93 X := X
% 6.55/6.93 Y := skol2
% 6.55/6.93 Z := skol3
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 subsumption: (10038) {G10,W11,D3,L3,V1,M1} R(914,74) { ! convergent_lines(
% 6.55/6.93 X, skol2 ), ! distinct_points( intersection_point( X, skol2 ), skol3 ),
% 6.55/6.93 apart_point_and_line( skol3, X ) }.
% 6.55/6.93 parent0: (10333) {G2,W11,D3,L3,V1,M3} { ! convergent_lines( X, skol2 ), !
% 6.55/6.93 distinct_points( intersection_point( X, skol2 ), skol3 ),
% 6.55/6.93 apart_point_and_line( skol3, X ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 X := X
% 6.55/6.93 end
% 6.55/6.93 permutation0:
% 6.55/6.93 0 ==> 0
% 6.55/6.93 1 ==> 1
% 6.55/6.93 2 ==> 2
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 resolution: (10335) {G2,W8,D3,L2,V0,M2} { ! convergent_lines( skol1, skol2
% 6.55/6.93 ), ! distinct_points( intersection_point( skol1, skol2 ), skol3 ) }.
% 6.55/6.93 parent0[0]: (73) {G1,W3,D2,L1,V0,M1} R(42,47) { ! apart_point_and_line(
% 6.55/6.93 skol3, skol1 ) }.
% 6.55/6.93 parent1[2]: (10038) {G10,W11,D3,L3,V1,M1} R(914,74) { ! convergent_lines( X
% 6.55/6.93 , skol2 ), ! distinct_points( intersection_point( X, skol2 ), skol3 ),
% 6.55/6.93 apart_point_and_line( skol3, X ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 end
% 6.55/6.93 substitution1:
% 6.55/6.93 X := skol1
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 resolution: (10336) {G1,W5,D3,L1,V0,M1} { ! distinct_points(
% 6.55/6.93 intersection_point( skol1, skol2 ), skol3 ) }.
% 6.55/6.93 parent0[0]: (10335) {G2,W8,D3,L2,V0,M2} { ! convergent_lines( skol1, skol2
% 6.55/6.93 ), ! distinct_points( intersection_point( skol1, skol2 ), skol3 ) }.
% 6.55/6.93 parent1[0]: (46) {G0,W3,D2,L1,V0,M1} I { convergent_lines( skol1, skol2 )
% 6.55/6.93 }.
% 6.55/6.93 substitution0:
% 6.55/6.93 end
% 6.55/6.93 substitution1:
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 subsumption: (10074) {G11,W5,D3,L1,V0,M1} R(10038,73);r(46) { !
% 6.55/6.93 distinct_points( intersection_point( skol1, skol2 ), skol3 ) }.
% 6.55/6.93 parent0: (10336) {G1,W5,D3,L1,V0,M1} { ! distinct_points(
% 6.55/6.93 intersection_point( skol1, skol2 ), skol3 ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 end
% 6.55/6.93 permutation0:
% 6.55/6.93 0 ==> 0
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 resolution: (10337) {G3,W0,D0,L0,V0,M0} { }.
% 6.55/6.93 parent0[0]: (10074) {G11,W5,D3,L1,V0,M1} R(10038,73);r(46) { !
% 6.55/6.93 distinct_points( intersection_point( skol1, skol2 ), skol3 ) }.
% 6.55/6.93 parent1[0]: (76) {G2,W5,D3,L1,V0,M1} R(75,52) { distinct_points(
% 6.55/6.93 intersection_point( skol1, skol2 ), skol3 ) }.
% 6.55/6.93 substitution0:
% 6.55/6.93 end
% 6.55/6.93 substitution1:
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 subsumption: (10079) {G12,W0,D0,L0,V0,M0} S(10074);r(76) { }.
% 6.55/6.93 parent0: (10337) {G3,W0,D0,L0,V0,M0} { }.
% 6.55/6.93 substitution0:
% 6.55/6.93 end
% 6.55/6.93 permutation0:
% 6.55/6.93 end
% 6.55/6.93
% 6.55/6.93 Proof check complete!
% 6.55/6.93
% 6.55/6.93 Memory use:
% 6.55/6.93
% 6.55/6.93 space for terms: 146430
% 6.55/6.93 space for clauses: 460857
% 6.55/6.93
% 6.55/6.93
% 6.55/6.93 clauses generated: 1013999
% 6.55/6.93 clauses kept: 10080
% 6.55/6.93 clauses selected: 2123
% 6.55/6.93 clauses deleted: 23
% 6.55/6.93 clauses inuse deleted: 3
% 6.55/6.93
% 6.55/6.93 subsentry: 10406871
% 6.55/6.93 literals s-matched: 4198312
% 6.55/6.93 literals matched: 4197768
% 6.55/6.93 full subsumption: 2833358
% 6.55/6.93
% 6.55/6.93 checksum: 2087175756
% 6.55/6.93
% 6.55/6.93
% 6.55/6.93 Bliksem ended
%------------------------------------------------------------------------------