TSTP Solution File: GEO170+3 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO170+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n017.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 02:52:12 EDT 2022
% Result : Theorem 1.24s 1.68s
% Output : Refutation 1.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO170+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Sat Jun 18 15:08:12 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.24/1.68 *** allocated 10000 integers for termspace/termends
% 1.24/1.68 *** allocated 10000 integers for clauses
% 1.24/1.68 *** allocated 10000 integers for justifications
% 1.24/1.68 Bliksem 1.12
% 1.24/1.68
% 1.24/1.68
% 1.24/1.68 Automatic Strategy Selection
% 1.24/1.68
% 1.24/1.68
% 1.24/1.68 Clauses:
% 1.24/1.68
% 1.24/1.68 { ! distinct_points( X, X ) }.
% 1.24/1.68 { ! distinct_lines( X, X ) }.
% 1.24/1.68 { ! convergent_lines( X, X ) }.
% 1.24/1.68 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 1.24/1.68 ) }.
% 1.24/1.68 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 1.24/1.68 }.
% 1.24/1.68 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 1.24/1.68 , Z ) }.
% 1.24/1.68 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 1.24/1.68 , Y ) ) }.
% 1.24/1.68 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 1.24/1.68 , Y ) ) }.
% 1.24/1.68 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 1.24/1.68 , Y ), X ) }.
% 1.24/1.68 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 1.24/1.68 , Y ), Y ) }.
% 1.24/1.68 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 1.24/1.68 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 1.24/1.68 apart_point_and_line( Y, T ) }.
% 1.24/1.68 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 1.24/1.68 apart_point_and_line( Z, Y ) }.
% 1.24/1.68 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 1.24/1.68 apart_point_and_line( X, Z ) }.
% 1.24/1.68 { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X,
% 1.24/1.68 Z ) }.
% 1.24/1.68 { ! distinct_lines( X, Y ), convergent_lines( X, Y ) }.
% 1.24/1.68 { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 1.24/1.68 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 1.24/1.68 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 1.24/1.68 apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 1.24/1.68 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 1.24/1.68 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 1.24/1.68 , convergent_lines( Y, Z ) }.
% 1.24/1.68 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 1.24/1.68 , unorthogonal_lines( Y, Z ) }.
% 1.24/1.68 { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 1.24/1.68 { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 1.24/1.68 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 1.24/1.68 }.
% 1.24/1.68 { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 1.24/1.68 { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 1.24/1.68 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 1.24/1.68 apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ),
% 1.24/1.68 unorthogonal_lines( Y, T ) }.
% 1.24/1.68 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 1.24/1.68 { alpha2( X, Z ), convergent_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 1.24/1.68 unorthogonal_lines( X, Y ) }.
% 1.24/1.68 { alpha2( X, Z ), unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 1.24/1.68 unorthogonal_lines( X, Y ) }.
% 1.24/1.68 { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 1.24/1.68 { ! alpha2( X, Y ), unorthogonal_lines( Y, X ) }.
% 1.24/1.68 { ! convergent_lines( Y, X ), ! unorthogonal_lines( Y, X ), alpha2( X, Y )
% 1.24/1.68 }.
% 1.24/1.68 { unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ), !
% 1.24/1.68 convergent_lines( X, Y ) }.
% 1.24/1.68 { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line(
% 1.24/1.68 line_connecting( X, Y ) ) }.
% 1.24/1.68 { ! line( X ), ! line( Y ), ! convergent_lines( X, Y ), point(
% 1.24/1.68 intersection_point( X, Y ) ) }.
% 1.24/1.68 { ! line( X ), ! point( Y ), line( parallel_through_point( X, Y ) ) }.
% 1.24/1.68 { ! line( X ), ! point( Y ), line( orthogonal_through_point( X, Y ) ) }.
% 1.24/1.68 { ! equal_points( X, Y ), ! distinct_points( X, Y ) }.
% 1.24/1.68 { distinct_points( X, Y ), equal_points( X, Y ) }.
% 1.24/1.68 { ! equal_lines( X, Y ), ! distinct_lines( X, Y ) }.
% 1.24/1.68 { distinct_lines( X, Y ), equal_lines( X, Y ) }.
% 1.24/1.68 { ! parallel_lines( X, Y ), ! convergent_lines( X, Y ) }.
% 1.24/1.68 { convergent_lines( X, Y ), parallel_lines( X, Y ) }.
% 1.24/1.68 { ! incident_point_and_line( X, Y ), ! apart_point_and_line( X, Y ) }.
% 1.24/1.68 { apart_point_and_line( X, Y ), incident_point_and_line( X, Y ) }.
% 1.24/1.68 { ! orthogonal_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 1.24/1.68 { unorthogonal_lines( X, Y ), orthogonal_lines( X, Y ) }.
% 1.24/1.68 { distinct_points( skol1, skol2 ) }.
% 1.24/1.68 { incident_point_and_line( skol1, skol3 ) }.
% 1.24/1.68 { incident_point_and_line( skol2, skol3 ) }.
% 1.24/1.68 { ! equal_lines( skol3, line_connecting( skol1, skol2 ) ) }.
% 1.24/1.68
% 1.24/1.68 percentage equality = 0.000000, percentage horn = 0.620000
% 1.24/1.68 This a non-horn, non-equality problem
% 1.24/1.68
% 1.24/1.68
% 1.24/1.68 Options Used:
% 1.24/1.68
% 1.24/1.68 useres = 1
% 1.24/1.68 useparamod = 0
% 1.24/1.68 useeqrefl = 0
% 1.24/1.68 useeqfact = 0
% 1.24/1.68 usefactor = 1
% 1.24/1.68 usesimpsplitting = 0
% 1.24/1.68 usesimpdemod = 0
% 1.24/1.68 usesimpres = 3
% 1.24/1.68
% 1.24/1.68 resimpinuse = 1000
% 1.24/1.68 resimpclauses = 20000
% 1.24/1.68 substype = standard
% 1.24/1.68 backwardsubs = 1
% 1.24/1.68 selectoldest = 5
% 1.24/1.68
% 1.24/1.68 litorderings [0] = split
% 1.24/1.68 litorderings [1] = liftord
% 1.24/1.68
% 1.24/1.68 termordering = none
% 1.24/1.68
% 1.24/1.68 litapriori = 1
% 1.24/1.68 termapriori = 0
% 1.24/1.68 litaposteriori = 0
% 1.24/1.68 termaposteriori = 0
% 1.24/1.68 demodaposteriori = 0
% 1.24/1.68 ordereqreflfact = 0
% 1.24/1.68
% 1.24/1.68 litselect = none
% 1.24/1.68
% 1.24/1.68 maxweight = 15
% 1.24/1.68 maxdepth = 30000
% 1.24/1.68 maxlength = 115
% 1.24/1.68 maxnrvars = 195
% 1.24/1.68 excuselevel = 1
% 1.24/1.68 increasemaxweight = 1
% 1.24/1.68
% 1.24/1.68 maxselected = 10000000
% 1.24/1.68 maxnrclauses = 10000000
% 1.24/1.68
% 1.24/1.68 showgenerated = 0
% 1.24/1.68 showkept = 0
% 1.24/1.68 showselected = 0
% 1.24/1.68 showdeleted = 0
% 1.24/1.68 showresimp = 1
% 1.24/1.68 showstatus = 2000
% 1.24/1.68
% 1.24/1.68 prologoutput = 0
% 1.24/1.68 nrgoals = 5000000
% 1.24/1.68 totalproof = 1
% 1.24/1.68
% 1.24/1.68 Symbols occurring in the translation:
% 1.24/1.68
% 1.24/1.68 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.24/1.68 . [1, 2] (w:1, o:26, a:1, s:1, b:0),
% 1.24/1.68 ! [4, 1] (w:0, o:19, a:1, s:1, b:0),
% 1.24/1.68 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.24/1.68 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.24/1.68 distinct_points [36, 2] (w:1, o:51, a:1, s:1, b:0),
% 1.24/1.68 distinct_lines [37, 2] (w:1, o:52, a:1, s:1, b:0),
% 1.24/1.68 convergent_lines [38, 2] (w:1, o:50, a:1, s:1, b:0),
% 1.24/1.68 line_connecting [41, 2] (w:1, o:53, a:1, s:1, b:0),
% 1.24/1.68 apart_point_and_line [42, 2] (w:1, o:54, a:1, s:1, b:0),
% 1.24/1.68 intersection_point [43, 2] (w:1, o:55, a:1, s:1, b:0),
% 1.24/1.68 parallel_through_point [46, 2] (w:1, o:58, a:1, s:1, b:0),
% 1.24/1.68 unorthogonal_lines [49, 2] (w:1, o:59, a:1, s:1, b:0),
% 1.24/1.68 orthogonal_through_point [52, 2] (w:1, o:56, a:1, s:1, b:0),
% 1.24/1.68 point [54, 1] (w:1, o:24, a:1, s:1, b:0),
% 1.24/1.68 line [55, 1] (w:1, o:25, a:1, s:1, b:0),
% 1.24/1.68 equal_points [56, 2] (w:1, o:60, a:1, s:1, b:0),
% 1.24/1.68 equal_lines [57, 2] (w:1, o:61, a:1, s:1, b:0),
% 1.24/1.68 parallel_lines [58, 2] (w:1, o:62, a:1, s:1, b:0),
% 1.24/1.68 incident_point_and_line [59, 2] (w:1, o:63, a:1, s:1, b:0),
% 1.24/1.68 orthogonal_lines [60, 2] (w:1, o:57, a:1, s:1, b:0),
% 1.24/1.68 alpha1 [61, 2] (w:1, o:64, a:1, s:1, b:0),
% 1.24/1.68 alpha2 [62, 2] (w:1, o:65, a:1, s:1, b:0),
% 1.24/1.68 skol1 [63, 0] (w:1, o:16, a:1, s:1, b:0),
% 1.24/1.68 skol2 [64, 0] (w:1, o:17, a:1, s:1, b:0),
% 1.24/1.68 skol3 [65, 0] (w:1, o:18, a:1, s:1, b:0).
% 1.24/1.68
% 1.24/1.68
% 1.24/1.68 Starting Search:
% 1.24/1.68
% 1.24/1.68 *** allocated 15000 integers for clauses
% 1.24/1.68 *** allocated 22500 integers for clauses
% 1.24/1.68 *** allocated 33750 integers for clauses
% 1.24/1.68 *** allocated 15000 integers for termspace/termends
% 1.24/1.68 *** allocated 50625 integers for clauses
% 1.24/1.68 Resimplifying inuse:
% 1.24/1.68 Done
% 1.24/1.68
% 1.24/1.68 *** allocated 22500 integers for termspace/termends
% 1.24/1.68 *** allocated 75937 integers for clauses
% 1.24/1.68 *** allocated 33750 integers for termspace/termends
% 1.24/1.68 *** allocated 113905 integers for clauses
% 1.24/1.68
% 1.24/1.68 Intermediate Status:
% 1.24/1.68 Generated: 14312
% 1.24/1.68 Kept: 2031
% 1.24/1.68 Inuse: 329
% 1.24/1.68 Deleted: 2
% 1.24/1.68 Deletedinuse: 2
% 1.24/1.68
% 1.24/1.68 Resimplifying inuse:
% 1.24/1.68 Done
% 1.24/1.68
% 1.24/1.68 *** allocated 50625 integers for termspace/termends
% 1.24/1.68 *** allocated 170857 integers for clauses
% 1.24/1.68 Resimplifying inuse:
% 1.24/1.68 Done
% 1.24/1.68
% 1.24/1.68 *** allocated 75937 integers for termspace/termends
% 1.24/1.68 *** allocated 256285 integers for clauses
% 1.24/1.68
% 1.24/1.68 Intermediate Status:
% 1.24/1.68 Generated: 36270
% 1.24/1.68 Kept: 4167
% 1.24/1.68 Inuse: 484
% 1.24/1.68 Deleted: 5
% 1.24/1.68 Deletedinuse: 2
% 1.24/1.68
% 1.24/1.68 Resimplifying inuse:
% 1.24/1.68 Done
% 1.24/1.68
% 1.24/1.68 *** allocated 113905 integers for termspace/termends
% 1.24/1.68 Resimplifying inuse:
% 1.24/1.68 Done
% 1.24/1.68
% 1.24/1.68
% 1.24/1.68 Bliksems!, er is een bewijs:
% 1.24/1.68 % SZS status Theorem
% 1.24/1.68 % SZS output start Refutation
% 1.24/1.68
% 1.24/1.68 (6) {G0,W8,D3,L2,V2,M1} I { ! distinct_points( X, Y ), !
% 1.24/1.68 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.24/1.68 (7) {G0,W8,D3,L2,V2,M1} I { ! distinct_points( X, Y ), !
% 1.24/1.68 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 1.24/1.68 (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), ! distinct_lines(
% 1.24/1.68 Z, T ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 1.24/1.68 apart_point_and_line( Y, T ), apart_point_and_line( X, Z ) }.
% 1.24/1.68 (39) {G0,W6,D2,L2,V2,M1} I { distinct_lines( X, Y ), equal_lines( X, Y )
% 1.24/1.68 }.
% 1.24/1.68 (42) {G0,W6,D2,L2,V2,M1} I { ! apart_point_and_line( X, Y ), !
% 1.24/1.68 incident_point_and_line( X, Y ) }.
% 1.24/1.68 (46) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol1, skol2 ) }.
% 1.24/1.68 (47) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol1, skol3 ) }.
% 1.24/1.68 (48) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol2, skol3 ) }.
% 1.24/1.68 (49) {G0,W5,D3,L1,V0,M1} I { ! equal_lines( skol3, line_connecting( skol1,
% 1.24/1.68 skol2 ) ) }.
% 1.24/1.68 (73) {G1,W3,D2,L1,V0,M1} R(42,47) { ! apart_point_and_line( skol1, skol3 )
% 1.24/1.68 }.
% 1.24/1.68 (74) {G1,W3,D2,L1,V0,M1} R(42,48) { ! apart_point_and_line( skol2, skol3 )
% 1.24/1.68 }.
% 1.24/1.68 (75) {G1,W5,D3,L1,V0,M1} R(39,49) { distinct_lines( skol3, line_connecting
% 1.24/1.68 ( skol1, skol2 ) ) }.
% 1.24/1.68 (98) {G1,W22,D3,L6,V4,M3} R(10,6) { ! distinct_points( X, Y ), !
% 1.24/1.68 distinct_lines( Z, line_connecting( X, T ) ), ! distinct_points( X, T ),
% 1.24/1.68 apart_point_and_line( X, Z ), apart_point_and_line( Y, Z ),
% 1.24/1.68 apart_point_and_line( Y, line_connecting( X, T ) ) }.
% 1.24/1.68 (111) {G2,W14,D3,L4,V3,M2} F(98);r(7) { ! distinct_points( X, Y ), !
% 1.24/1.68 distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line( Y, Z
% 1.24/1.68 ), apart_point_and_line( X, Z ) }.
% 1.24/1.68 (2254) {G3,W11,D3,L3,V1,M1} R(111,74) { ! distinct_points( X, skol2 ), !
% 1.24/1.68 distinct_lines( skol3, line_connecting( X, skol2 ) ),
% 1.24/1.68 apart_point_and_line( X, skol3 ) }.
% 1.24/1.68 (5466) {G4,W5,D3,L1,V0,M1} R(2254,73);r(46) { ! distinct_lines( skol3,
% 1.24/1.68 line_connecting( skol1, skol2 ) ) }.
% 1.24/1.68 (5467) {G5,W0,D0,L0,V0,M0} S(5466);r(75) { }.
% 1.24/1.68
% 1.24/1.68
% 1.24/1.68 % SZS output end Refutation
% 1.24/1.68 found a proof!
% 1.24/1.68
% 1.24/1.68
% 1.24/1.68 Unprocessed initial clauses:
% 1.24/1.68
% 1.24/1.68 (5469) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 1.24/1.68 (5470) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 1.24/1.68 (5471) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 1.24/1.68 (5472) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 1.24/1.68 , Z ), distinct_points( Y, Z ) }.
% 1.24/1.68 (5473) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X,
% 1.24/1.68 Z ), distinct_lines( Y, Z ) }.
% 1.24/1.68 (5474) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines
% 1.24/1.68 ( X, Z ), convergent_lines( Y, Z ) }.
% 1.24/1.68 (5475) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 1.24/1.68 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.24/1.68 (5476) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 1.24/1.68 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 1.24/1.68 (5477) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 1.24/1.68 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 1.24/1.68 (5478) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 1.24/1.68 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 1.24/1.68 (5479) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines
% 1.24/1.68 ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 1.24/1.68 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 1.24/1.68 (5480) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 1.24/1.68 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 1.24/1.68 (5481) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 1.24/1.68 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 1.24/1.68 (5482) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), distinct_lines( Y
% 1.24/1.68 , Z ), convergent_lines( X, Z ) }.
% 1.24/1.68 (5483) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ), convergent_lines( X
% 1.24/1.68 , Y ) }.
% 1.24/1.68 (5484) {G0,W5,D3,L1,V2,M1} { ! convergent_lines( parallel_through_point( Y
% 1.24/1.68 , X ), Y ) }.
% 1.24/1.68 (5485) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 1.24/1.68 parallel_through_point( Y, X ) ) }.
% 1.24/1.68 (5486) {G0,W12,D2,L4,V3,M4} { ! distinct_lines( X, Y ),
% 1.24/1.68 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 1.24/1.68 convergent_lines( X, Y ) }.
% 1.24/1.68 (5487) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines
% 1.24/1.68 ( X, Y ) }.
% 1.24/1.68 (5488) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 1.24/1.68 unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 1.24/1.68 (5489) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 1.24/1.68 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 1.24/1.68 }.
% 1.24/1.68 (5490) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines( X, Y )
% 1.24/1.68 }.
% 1.24/1.68 (5491) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 1.24/1.68 }.
% 1.24/1.68 (5492) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( X, Y ), !
% 1.24/1.68 unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 1.24/1.68 (5493) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines(
% 1.24/1.68 orthogonal_through_point( Y, X ), Y ) }.
% 1.24/1.68 (5494) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 1.24/1.68 orthogonal_through_point( Y, X ) ) }.
% 1.24/1.68 (5495) {G0,W15,D2,L5,V4,M5} { ! distinct_lines( X, Y ),
% 1.24/1.68 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 1.24/1.68 unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 1.24/1.68 (5496) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines
% 1.24/1.68 ( X, Y ) }.
% 1.24/1.68 (5497) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), convergent_lines( Z, Y ), !
% 1.24/1.68 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 1.24/1.68 (5498) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), unorthogonal_lines( Z, Y ),
% 1.24/1.68 ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 1.24/1.68 (5499) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), convergent_lines( Y, X )
% 1.24/1.68 }.
% 1.24/1.68 (5500) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), unorthogonal_lines( Y, X )
% 1.24/1.68 }.
% 1.24/1.68 (5501) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( Y, X ), !
% 1.24/1.68 unorthogonal_lines( Y, X ), alpha2( X, Y ) }.
% 1.24/1.68 (5502) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ),
% 1.24/1.68 unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 1.24/1.68 (5503) {G0,W11,D3,L4,V2,M4} { ! point( X ), ! point( Y ), !
% 1.24/1.68 distinct_points( X, Y ), line( line_connecting( X, Y ) ) }.
% 1.24/1.68 (5504) {G0,W11,D3,L4,V2,M4} { ! line( X ), ! line( Y ), ! convergent_lines
% 1.24/1.68 ( X, Y ), point( intersection_point( X, Y ) ) }.
% 1.24/1.68 (5505) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 1.24/1.68 parallel_through_point( X, Y ) ) }.
% 1.24/1.68 (5506) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 1.24/1.68 orthogonal_through_point( X, Y ) ) }.
% 1.24/1.68 (5507) {G0,W6,D2,L2,V2,M2} { ! equal_points( X, Y ), ! distinct_points( X
% 1.24/1.68 , Y ) }.
% 1.24/1.68 (5508) {G0,W6,D2,L2,V2,M2} { distinct_points( X, Y ), equal_points( X, Y )
% 1.24/1.68 }.
% 1.24/1.68 (5509) {G0,W6,D2,L2,V2,M2} { ! equal_lines( X, Y ), ! distinct_lines( X, Y
% 1.24/1.68 ) }.
% 1.24/1.68 (5510) {G0,W6,D2,L2,V2,M2} { distinct_lines( X, Y ), equal_lines( X, Y )
% 1.24/1.68 }.
% 1.24/1.68 (5511) {G0,W6,D2,L2,V2,M2} { ! parallel_lines( X, Y ), ! convergent_lines
% 1.24/1.68 ( X, Y ) }.
% 1.24/1.68 (5512) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), parallel_lines( X,
% 1.24/1.68 Y ) }.
% 1.24/1.68 (5513) {G0,W6,D2,L2,V2,M2} { ! incident_point_and_line( X, Y ), !
% 1.24/1.68 apart_point_and_line( X, Y ) }.
% 1.24/1.68 (5514) {G0,W6,D2,L2,V2,M2} { apart_point_and_line( X, Y ),
% 1.24/1.68 incident_point_and_line( X, Y ) }.
% 1.24/1.68 (5515) {G0,W6,D2,L2,V2,M2} { ! orthogonal_lines( X, Y ), !
% 1.24/1.68 unorthogonal_lines( X, Y ) }.
% 1.24/1.68 (5516) {G0,W6,D2,L2,V2,M2} { unorthogonal_lines( X, Y ), orthogonal_lines
% 1.24/1.68 ( X, Y ) }.
% 1.24/1.68 (5517) {G0,W3,D2,L1,V0,M1} { distinct_points( skol1, skol2 ) }.
% 1.24/1.68 (5518) {G0,W3,D2,L1,V0,M1} { incident_point_and_line( skol1, skol3 ) }.
% 1.24/1.68 (5519) {G0,W3,D2,L1,V0,M1} { incident_point_and_line( skol2, skol3 ) }.
% 1.24/1.68 (5520) {G0,W5,D3,L1,V0,M1} { ! equal_lines( skol3, line_connecting( skol1
% 1.24/1.68 , skol2 ) ) }.
% 1.24/1.68
% 1.24/1.68
% 1.24/1.68 Total Proof:
% 1.24/1.68
% 1.24/1.68 subsumption: (6) {G0,W8,D3,L2,V2,M1} I { ! distinct_points( X, Y ), !
% 1.24/1.68 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.24/1.68 parent0: (5475) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 1.24/1.68 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.24/1.68 substitution0:
% 1.24/1.68 X := X
% 1.24/1.68 Y := Y
% 1.24/1.68 end
% 1.24/1.68 permutation0:
% 1.24/1.68 0 ==> 0
% 1.24/1.68 1 ==> 1
% 1.24/1.68 end
% 1.24/1.68
% 1.24/1.68 subsumption: (7) {G0,W8,D3,L2,V2,M1} I { ! distinct_points( X, Y ), !
% 1.24/1.68 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 1.24/1.68 parent0: (5476) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 1.24/1.68 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 1.24/1.68 substitution0:
% 1.24/1.68 X := X
% 1.24/1.68 Y := Y
% 1.24/1.68 end
% 1.24/1.68 permutation0:
% 1.24/1.68 0 ==> 0
% 1.24/1.68 1 ==> 1
% 1.24/1.68 end
% 1.24/1.68
% 1.24/1.68 subsumption: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), !
% 1.24/1.68 distinct_lines( Z, T ), apart_point_and_line( X, T ),
% 1.24/1.68 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ),
% 1.24/1.68 apart_point_and_line( X, Z ) }.
% 1.24/1.68 parent0: (5479) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), !
% 1.24/1.68 distinct_lines( Z, T ), apart_point_and_line( X, Z ),
% 1.24/1.68 apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 1.24/1.68 apart_point_and_line( Y, T ) }.
% 1.24/1.68 substitution0:
% 1.24/1.68 X := X
% 1.24/1.68 Y := Y
% 1.24/1.68 Z := Z
% 1.24/1.68 T := T
% 1.24/1.68 end
% 1.24/1.68 permutation0:
% 1.24/1.68 0 ==> 0
% 1.24/1.68 1 ==> 1
% 1.24/1.68 2 ==> 5
% 1.24/1.68 3 ==> 2
% 1.24/1.68 4 ==> 3
% 1.24/1.68 5 ==> 4
% 1.24/1.68 end
% 1.24/1.68
% 1.24/1.68 subsumption: (39) {G0,W6,D2,L2,V2,M1} I { distinct_lines( X, Y ),
% 1.24/1.68 equal_lines( X, Y ) }.
% 1.24/1.68 parent0: (5510) {G0,W6,D2,L2,V2,M2} { distinct_lines( X, Y ), equal_lines
% 1.24/1.68 ( X, Y ) }.
% 1.24/1.68 substitution0:
% 1.24/1.68 X := X
% 1.24/1.68 Y := Y
% 1.24/1.68 end
% 1.24/1.68 permutation0:
% 1.24/1.68 0 ==> 0
% 1.24/1.68 1 ==> 1
% 1.24/1.68 end
% 1.24/1.68
% 1.24/1.68 subsumption: (42) {G0,W6,D2,L2,V2,M1} I { ! apart_point_and_line( X, Y ), !
% 1.24/1.68 incident_point_and_line( X, Y ) }.
% 1.24/1.68 parent0: (5513) {G0,W6,D2,L2,V2,M2} { ! incident_point_and_line( X, Y ), !
% 1.24/1.68 apart_point_and_line( X, Y ) }.
% 1.24/1.68 substitution0:
% 1.24/1.68 X := X
% 1.24/1.68 Y := Y
% 1.24/1.68 end
% 1.24/1.68 permutation0:
% 1.24/1.68 0 ==> 1
% 1.24/1.68 1 ==> 0
% 1.24/1.68 end
% 1.24/1.68
% 1.24/1.68 subsumption: (46) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol1, skol2 )
% 1.24/1.68 }.
% 1.24/1.68 parent0: (5517) {G0,W3,D2,L1,V0,M1} { distinct_points( skol1, skol2 ) }.
% 1.24/1.68 substitution0:
% 1.24/1.68 end
% 1.24/1.68 permutation0:
% 1.24/1.68 0 ==> 0
% 1.24/1.68 end
% 1.24/1.68
% 1.24/1.68 subsumption: (47) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol1,
% 1.24/1.68 skol3 ) }.
% 1.24/1.68 parent0: (5518) {G0,W3,D2,L1,V0,M1} { incident_point_and_line( skol1,
% 1.24/1.68 skol3 ) }.
% 1.24/1.68 substitution0:
% 1.24/1.68 end
% 1.24/1.68 permutation0:
% 1.24/1.68 0 ==> 0
% 1.24/1.68 end
% 1.24/1.68
% 1.24/1.68 subsumption: (48) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol2,
% 1.24/1.68 skol3 ) }.
% 1.24/1.68 parent0: (5519) {G0,W3,D2,L1,V0,M1} { incident_point_and_line( skol2,
% 1.24/1.68 skol3 ) }.
% 1.24/1.68 substitution0:
% 1.24/1.68 end
% 1.24/1.68 permutation0:
% 1.24/1.68 0 ==> 0
% 1.24/1.68 end
% 1.24/1.68
% 1.24/1.68 subsumption: (49) {G0,W5,D3,L1,V0,M1} I { ! equal_lines( skol3,
% 1.24/1.68 line_connecting( skol1, skol2 ) ) }.
% 1.24/1.68 parent0: (5520) {G0,W5,D3,L1,V0,M1} { ! equal_lines( skol3,
% 1.24/1.68 line_connecting( skol1, skol2 ) ) }.
% 1.24/1.68 substitution0:
% 1.24/1.68 end
% 1.24/1.68 permutation0:
% 1.24/1.68 0 ==> 0
% 1.24/1.68 end
% 1.24/1.68
% 1.24/1.68 resolution: (5626) {G1,W3,D2,L1,V0,M1} { ! apart_point_and_line( skol1,
% 1.24/1.68 skol3 ) }.
% 1.24/1.68 parent0[1]: (42) {G0,W6,D2,L2,V2,M1} I { ! apart_point_and_line( X, Y ), !
% 1.24/1.68 incident_point_and_line( X, Y ) }.
% 1.24/1.68 parent1[0]: (47) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol1,
% 1.24/1.68 skol3 ) }.
% 1.24/1.68 substitution0:
% 1.24/1.68 X := skol1
% 1.24/1.68 Y := skol3
% 1.24/1.68 end
% 1.24/1.68 substitution1:
% 1.24/1.68 end
% 1.24/1.68
% 1.24/1.68 subsumption: (73) {G1,W3,D2,L1,V0,M1} R(42,47) { ! apart_point_and_line(
% 1.24/1.68 skol1, skol3 ) }.
% 1.24/1.68 parent0: (5626) {G1,W3,D2,L1,V0,M1} { ! apart_point_and_line( skol1, skol3
% 1.24/1.68 ) }.
% 1.24/1.68 substitution0:
% 1.24/1.68 end
% 1.24/1.68 permutation0:
% 1.24/1.68 0 ==> 0
% 1.24/1.68 end
% 1.24/1.68
% 1.24/1.68 resolution: (5627) {G1,W3,D2,L1,V0,M1} { ! apart_point_and_line( skol2,
% 1.24/1.68 skol3 ) }.
% 1.24/1.68 parent0[1]: (42) {G0,W6,D2,L2,V2,M1} I { ! apart_point_and_line( X, Y ), !
% 1.24/1.68 incident_point_and_line( X, Y ) }.
% 1.24/1.68 parent1[0]: (48) {G0,W3,D2,L1,V0,M1} I { incident_point_and_line( skol2,
% 1.24/1.68 skol3 ) }.
% 1.24/1.68 substitution0:
% 1.24/1.68 X := skol2
% 1.24/1.68 Y := skol3
% 1.24/1.68 end
% 1.24/1.68 substitution1:
% 1.24/1.68 end
% 1.24/1.68
% 1.24/1.68 subsumption: (74) {G1,W3,D2,L1,V0,M1} R(42,48) { ! apart_point_and_line(
% 1.24/1.68 skol2, skol3 ) }.
% 1.24/1.68 parent0: (5627) {G1,W3,D2,L1,V0,M1} { ! apart_point_and_line( skol2, skol3
% 1.24/1.68 ) }.
% 1.24/1.68 substitution0:
% 1.24/1.68 end
% 1.24/1.68 permutation0:
% 1.24/1.68 0 ==> 0
% 1.24/1.68 end
% 1.24/1.68
% 1.24/1.68 resolution: (5628) {G1,W5,D3,L1,V0,M1} { distinct_lines( skol3,
% 1.24/1.68 line_connecting( skol1, skol2 ) ) }.
% 1.24/1.68 parent0[0]: (49) {G0,W5,D3,L1,V0,M1} I { ! equal_lines( skol3,
% 1.24/1.68 line_connecting( skol1, skol2 ) ) }.
% 1.24/1.68 parent1[1]: (39) {G0,W6,D2,L2,V2,M1} I { distinct_lines( X, Y ),
% 1.24/1.68 equal_lines( X, Y ) }.
% 1.24/1.68 substitution0:
% 1.24/1.68 end
% 1.24/1.68 substitution1:
% 1.24/1.68 X := skol3
% 1.24/1.68 Y := line_connecting( skol1, skol2 )
% 1.24/1.68 end
% 1.24/1.68
% 1.24/1.68 subsumption: (75) {G1,W5,D3,L1,V0,M1} R(39,49) { distinct_lines( skol3,
% 1.24/1.68 line_connecting( skol1, skol2 ) ) }.
% 1.31/1.68 parent0: (5628) {G1,W5,D3,L1,V0,M1} { distinct_lines( skol3,
% 1.31/1.68 line_connecting( skol1, skol2 ) ) }.
% 1.31/1.68 substitution0:
% 1.31/1.68 end
% 1.31/1.68 permutation0:
% 1.31/1.68 0 ==> 0
% 1.31/1.68 end
% 1.31/1.68
% 1.31/1.68 resolution: (5629) {G1,W22,D3,L6,V4,M6} { ! distinct_points( X, Y ), !
% 1.31/1.68 distinct_points( X, Z ), ! distinct_lines( T, line_connecting( X, Y ) ),
% 1.31/1.68 apart_point_and_line( Z, T ), apart_point_and_line( Z, line_connecting( X
% 1.31/1.68 , Y ) ), apart_point_and_line( X, T ) }.
% 1.31/1.68 parent0[1]: (6) {G0,W8,D3,L2,V2,M1} I { ! distinct_points( X, Y ), !
% 1.31/1.68 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 1.31/1.68 parent1[2]: (10) {G0,W18,D2,L6,V4,M4} I { ! distinct_points( X, Y ), !
% 1.31/1.68 distinct_lines( Z, T ), apart_point_and_line( X, T ),
% 1.31/1.68 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ),
% 1.31/1.68 apart_point_and_line( X, Z ) }.
% 1.31/1.68 substitution0:
% 1.31/1.68 X := X
% 1.31/1.68 Y := Y
% 1.31/1.68 end
% 1.31/1.68 substitution1:
% 1.31/1.68 X := X
% 1.31/1.68 Y := Z
% 1.31/1.68 Z := T
% 1.31/1.68 T := line_connecting( X, Y )
% 1.31/1.68 end
% 1.31/1.68
% 1.31/1.68 subsumption: (98) {G1,W22,D3,L6,V4,M3} R(10,6) { ! distinct_points( X, Y )
% 1.31/1.68 , ! distinct_lines( Z, line_connecting( X, T ) ), ! distinct_points( X, T
% 1.31/1.68 ), apart_point_and_line( X, Z ), apart_point_and_line( Y, Z ),
% 1.31/1.68 apart_point_and_line( Y, line_connecting( X, T ) ) }.
% 1.31/1.68 parent0: (5629) {G1,W22,D3,L6,V4,M6} { ! distinct_points( X, Y ), !
% 1.31/1.68 distinct_points( X, Z ), ! distinct_lines( T, line_connecting( X, Y ) ),
% 1.31/1.68 apart_point_and_line( Z, T ), apart_point_and_line( Z, line_connecting( X
% 1.31/1.68 , Y ) ), apart_point_and_line( X, T ) }.
% 1.31/1.68 substitution0:
% 1.31/1.68 X := X
% 1.31/1.68 Y := T
% 1.31/1.68 Z := Y
% 1.31/1.68 T := Z
% 1.31/1.68 end
% 1.31/1.68 permutation0:
% 1.31/1.68 0 ==> 2
% 1.31/1.68 1 ==> 0
% 1.31/1.68 2 ==> 1
% 1.31/1.68 3 ==> 4
% 1.31/1.68 4 ==> 5
% 1.31/1.68 5 ==> 3
% 1.31/1.68 end
% 1.31/1.68
% 1.31/1.68 factor: (5645) {G1,W19,D3,L5,V3,M5} { ! distinct_points( X, Y ), !
% 1.31/1.68 distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line( X, Z
% 1.31/1.68 ), apart_point_and_line( Y, Z ), apart_point_and_line( Y,
% 1.31/1.68 line_connecting( X, Y ) ) }.
% 1.31/1.68 parent0[0, 2]: (98) {G1,W22,D3,L6,V4,M3} R(10,6) { ! distinct_points( X, Y
% 1.31/1.68 ), ! distinct_lines( Z, line_connecting( X, T ) ), ! distinct_points( X
% 1.31/1.68 , T ), apart_point_and_line( X, Z ), apart_point_and_line( Y, Z ),
% 1.31/1.68 apart_point_and_line( Y, line_connecting( X, T ) ) }.
% 1.31/1.68 substitution0:
% 1.31/1.68 X := X
% 1.31/1.68 Y := Y
% 1.31/1.68 Z := Z
% 1.31/1.68 T := Y
% 1.31/1.68 end
% 1.31/1.68
% 1.31/1.68 resolution: (5652) {G1,W17,D3,L5,V3,M5} { ! distinct_points( X, Y ), !
% 1.31/1.68 distinct_points( X, Y ), ! distinct_lines( Z, line_connecting( X, Y ) ),
% 1.31/1.68 apart_point_and_line( X, Z ), apart_point_and_line( Y, Z ) }.
% 1.31/1.68 parent0[1]: (7) {G0,W8,D3,L2,V2,M1} I { ! distinct_points( X, Y ), !
% 1.31/1.68 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 1.31/1.68 parent1[4]: (5645) {G1,W19,D3,L5,V3,M5} { ! distinct_points( X, Y ), !
% 1.31/1.68 distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line( X, Z
% 1.31/1.68 ), apart_point_and_line( Y, Z ), apart_point_and_line( Y,
% 1.31/1.68 line_connecting( X, Y ) ) }.
% 1.31/1.68 substitution0:
% 1.31/1.68 X := X
% 1.31/1.68 Y := Y
% 1.31/1.68 end
% 1.31/1.68 substitution1:
% 1.31/1.68 X := X
% 1.31/1.68 Y := Y
% 1.31/1.68 Z := Z
% 1.31/1.68 end
% 1.31/1.68
% 1.31/1.68 factor: (5653) {G1,W14,D3,L4,V3,M4} { ! distinct_points( X, Y ), !
% 1.31/1.68 distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line( X, Z
% 1.31/1.68 ), apart_point_and_line( Y, Z ) }.
% 1.31/1.68 parent0[0, 1]: (5652) {G1,W17,D3,L5,V3,M5} { ! distinct_points( X, Y ), !
% 1.31/1.68 distinct_points( X, Y ), ! distinct_lines( Z, line_connecting( X, Y ) ),
% 1.31/1.68 apart_point_and_line( X, Z ), apart_point_and_line( Y, Z ) }.
% 1.31/1.68 substitution0:
% 1.31/1.68 X := X
% 1.31/1.68 Y := Y
% 1.31/1.68 Z := Z
% 1.31/1.68 end
% 1.31/1.68
% 1.31/1.68 subsumption: (111) {G2,W14,D3,L4,V3,M2} F(98);r(7) { ! distinct_points( X,
% 1.31/1.68 Y ), ! distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line
% 1.31/1.68 ( Y, Z ), apart_point_and_line( X, Z ) }.
% 1.31/1.68 parent0: (5653) {G1,W14,D3,L4,V3,M4} { ! distinct_points( X, Y ), !
% 1.31/1.68 distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line( X, Z
% 1.31/1.68 ), apart_point_and_line( Y, Z ) }.
% 1.31/1.68 substitution0:
% 1.31/1.68 X := X
% 1.31/1.68 Y := Y
% 1.31/1.68 Z := Z
% 1.31/1.68 end
% 1.31/1.68 permutation0:
% 1.31/1.68 0 ==> 0
% 1.31/1.68 1 ==> 1
% 1.31/1.68 2 ==> 3
% 1.31/1.68 3 ==> 2
% 1.31/1.68 end
% 1.31/1.68
% 1.31/1.68 resolution: (5655) {G2,W11,D3,L3,V1,M3} { ! distinct_points( X, skol2 ), !
% 1.31/1.68 distinct_lines( skol3, line_connecting( X, skol2 ) ),
% 1.31/1.68 apart_point_and_line( X, skol3 ) }.
% 1.31/1.68 parent0[0]: (74) {G1,W3,D2,L1,V0,M1} R(42,48) { ! apart_point_and_line(
% 1.31/1.68 skol2, skol3 ) }.
% 1.31/1.68 parent1[2]: (111) {G2,W14,D3,L4,V3,M2} F(98);r(7) { ! distinct_points( X, Y
% 1.31/1.68 ), ! distinct_lines( Z, line_connecting( X, Y ) ), apart_point_and_line
% 1.31/1.68 ( Y, Z ), apart_point_and_line( X, Z ) }.
% 1.31/1.68 substitution0:
% 1.31/1.68 end
% 1.31/1.68 substitution1:
% 1.31/1.68 X := X
% 1.31/1.68 Y := skol2
% 1.31/1.68 Z := skol3
% 1.31/1.68 end
% 1.31/1.68
% 1.31/1.68 subsumption: (2254) {G3,W11,D3,L3,V1,M1} R(111,74) { ! distinct_points( X,
% 1.31/1.68 skol2 ), ! distinct_lines( skol3, line_connecting( X, skol2 ) ),
% 1.31/1.68 apart_point_and_line( X, skol3 ) }.
% 1.31/1.68 parent0: (5655) {G2,W11,D3,L3,V1,M3} { ! distinct_points( X, skol2 ), !
% 1.31/1.68 distinct_lines( skol3, line_connecting( X, skol2 ) ),
% 1.31/1.68 apart_point_and_line( X, skol3 ) }.
% 1.31/1.68 substitution0:
% 1.31/1.68 X := X
% 1.31/1.68 end
% 1.31/1.68 permutation0:
% 1.31/1.68 0 ==> 0
% 1.31/1.68 1 ==> 1
% 1.31/1.68 2 ==> 2
% 1.31/1.68 end
% 1.31/1.68
% 1.31/1.68 resolution: (5657) {G2,W8,D3,L2,V0,M2} { ! distinct_points( skol1, skol2 )
% 1.31/1.68 , ! distinct_lines( skol3, line_connecting( skol1, skol2 ) ) }.
% 1.31/1.68 parent0[0]: (73) {G1,W3,D2,L1,V0,M1} R(42,47) { ! apart_point_and_line(
% 1.31/1.68 skol1, skol3 ) }.
% 1.31/1.68 parent1[2]: (2254) {G3,W11,D3,L3,V1,M1} R(111,74) { ! distinct_points( X,
% 1.31/1.68 skol2 ), ! distinct_lines( skol3, line_connecting( X, skol2 ) ),
% 1.31/1.68 apart_point_and_line( X, skol3 ) }.
% 1.31/1.68 substitution0:
% 1.31/1.68 end
% 1.31/1.68 substitution1:
% 1.31/1.68 X := skol1
% 1.31/1.68 end
% 1.31/1.68
% 1.31/1.68 resolution: (5658) {G1,W5,D3,L1,V0,M1} { ! distinct_lines( skol3,
% 1.31/1.68 line_connecting( skol1, skol2 ) ) }.
% 1.31/1.68 parent0[0]: (5657) {G2,W8,D3,L2,V0,M2} { ! distinct_points( skol1, skol2 )
% 1.31/1.68 , ! distinct_lines( skol3, line_connecting( skol1, skol2 ) ) }.
% 1.31/1.68 parent1[0]: (46) {G0,W3,D2,L1,V0,M1} I { distinct_points( skol1, skol2 )
% 1.31/1.68 }.
% 1.31/1.68 substitution0:
% 1.31/1.68 end
% 1.31/1.68 substitution1:
% 1.31/1.68 end
% 1.31/1.68
% 1.31/1.68 subsumption: (5466) {G4,W5,D3,L1,V0,M1} R(2254,73);r(46) { ! distinct_lines
% 1.31/1.68 ( skol3, line_connecting( skol1, skol2 ) ) }.
% 1.31/1.68 parent0: (5658) {G1,W5,D3,L1,V0,M1} { ! distinct_lines( skol3,
% 1.31/1.68 line_connecting( skol1, skol2 ) ) }.
% 1.31/1.68 substitution0:
% 1.31/1.68 end
% 1.31/1.68 permutation0:
% 1.31/1.68 0 ==> 0
% 1.31/1.68 end
% 1.31/1.68
% 1.31/1.68 resolution: (5659) {G2,W0,D0,L0,V0,M0} { }.
% 1.31/1.68 parent0[0]: (5466) {G4,W5,D3,L1,V0,M1} R(2254,73);r(46) { ! distinct_lines
% 1.31/1.68 ( skol3, line_connecting( skol1, skol2 ) ) }.
% 1.31/1.68 parent1[0]: (75) {G1,W5,D3,L1,V0,M1} R(39,49) { distinct_lines( skol3,
% 1.31/1.68 line_connecting( skol1, skol2 ) ) }.
% 1.31/1.68 substitution0:
% 1.31/1.68 end
% 1.31/1.68 substitution1:
% 1.31/1.68 end
% 1.31/1.68
% 1.31/1.68 subsumption: (5467) {G5,W0,D0,L0,V0,M0} S(5466);r(75) { }.
% 1.31/1.68 parent0: (5659) {G2,W0,D0,L0,V0,M0} { }.
% 1.31/1.68 substitution0:
% 1.31/1.68 end
% 1.31/1.68 permutation0:
% 1.31/1.68 end
% 1.31/1.68
% 1.31/1.68 Proof check complete!
% 1.31/1.68
% 1.31/1.68 Memory use:
% 1.31/1.68
% 1.31/1.68 space for terms: 78881
% 1.31/1.68 space for clauses: 227328
% 1.31/1.68
% 1.31/1.68
% 1.31/1.68 clauses generated: 49673
% 1.31/1.68 clauses kept: 5468
% 1.31/1.68 clauses selected: 614
% 1.31/1.68 clauses deleted: 7
% 1.31/1.68 clauses inuse deleted: 3
% 1.31/1.68
% 1.31/1.68 subsentry: 1017977
% 1.31/1.68 literals s-matched: 404706
% 1.31/1.68 literals matched: 404265
% 1.31/1.68 full subsumption: 248508
% 1.31/1.68
% 1.31/1.68 checksum: 629294311
% 1.31/1.68
% 1.31/1.68
% 1.31/1.68 Bliksem ended
%------------------------------------------------------------------------------