TSTP Solution File: GEO210+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO210+1 : TPTP v8.1.0. Released v3.3.0.
% 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 02:52:47 EDT 2022
% Result : Theorem 14.77s 15.20s
% Output : Refutation 14.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO210+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : bliksem %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Sat Jun 18 05:14:57 EDT 2022
% 0.13/0.34 % CPUTime :
% 14.77/15.20 *** allocated 10000 integers for termspace/termends
% 14.77/15.20 *** allocated 10000 integers for clauses
% 14.77/15.20 *** allocated 10000 integers for justifications
% 14.77/15.20 Bliksem 1.12
% 14.77/15.20
% 14.77/15.20
% 14.77/15.20 Automatic Strategy Selection
% 14.77/15.20
% 14.77/15.20
% 14.77/15.20 Clauses:
% 14.77/15.20
% 14.77/15.20 { ! distinct_points( X, X ) }.
% 14.77/15.20 { ! distinct_lines( X, X ) }.
% 14.77/15.20 { ! convergent_lines( X, X ) }.
% 14.77/15.20 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 14.77/15.20 ) }.
% 14.77/15.20 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 14.77/15.20 }.
% 14.77/15.20 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 14.77/15.20 , Z ) }.
% 14.77/15.20 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 14.77/15.20 , Y ) ) }.
% 14.77/15.20 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 14.77/15.20 , Y ) ) }.
% 14.77/15.20 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 14.77/15.20 , Y ), X ) }.
% 14.77/15.20 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 14.77/15.20 , Y ), Y ) }.
% 14.77/15.20 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 14.77/15.20 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 14.77/15.20 apart_point_and_line( Y, T ) }.
% 14.77/15.20 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 14.77/15.20 apart_point_and_line( Z, Y ) }.
% 14.77/15.20 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 14.77/15.20 apart_point_and_line( X, Z ) }.
% 14.77/15.20 { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X,
% 14.77/15.20 Z ) }.
% 14.77/15.20 { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 14.77/15.20 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 14.77/15.20 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 14.77/15.20 apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 14.77/15.20 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 14.77/15.20 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 14.77/15.20 , convergent_lines( Y, Z ) }.
% 14.77/15.20 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 14.77/15.20 , unorthogonal_lines( Y, Z ) }.
% 14.77/15.20 { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 14.77/15.20 { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 14.77/15.20 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 14.77/15.20 }.
% 14.77/15.20 { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 14.77/15.20 { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 14.77/15.20 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 14.77/15.20 apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ),
% 14.77/15.20 unorthogonal_lines( Y, T ) }.
% 14.77/15.20 { ! apart_point_and_line( skol1, skol2 ) }.
% 14.77/15.20 { ! unorthogonal_lines( skol2, skol3 ) }.
% 14.77/15.20 { distinct_lines( skol2, orthogonal_through_point( skol3, skol1 ) ) }.
% 14.77/15.20
% 14.77/15.20 percentage equality = 0.000000, percentage horn = 0.586207
% 14.77/15.20 This a non-horn, non-equality problem
% 14.77/15.20
% 14.77/15.20
% 14.77/15.20 Options Used:
% 14.77/15.20
% 14.77/15.20 useres = 1
% 14.77/15.20 useparamod = 0
% 14.77/15.20 useeqrefl = 0
% 14.77/15.20 useeqfact = 0
% 14.77/15.20 usefactor = 1
% 14.77/15.20 usesimpsplitting = 0
% 14.77/15.20 usesimpdemod = 0
% 14.77/15.20 usesimpres = 3
% 14.77/15.20
% 14.77/15.20 resimpinuse = 1000
% 14.77/15.20 resimpclauses = 20000
% 14.77/15.20 substype = standard
% 14.77/15.20 backwardsubs = 1
% 14.77/15.20 selectoldest = 5
% 14.77/15.20
% 14.77/15.20 litorderings [0] = split
% 14.77/15.20 litorderings [1] = liftord
% 14.77/15.20
% 14.77/15.20 termordering = none
% 14.77/15.20
% 14.77/15.20 litapriori = 1
% 14.77/15.20 termapriori = 0
% 14.77/15.20 litaposteriori = 0
% 14.77/15.20 termaposteriori = 0
% 14.77/15.20 demodaposteriori = 0
% 14.77/15.20 ordereqreflfact = 0
% 14.77/15.20
% 14.77/15.20 litselect = none
% 14.77/15.20
% 14.77/15.20 maxweight = 15
% 14.77/15.20 maxdepth = 30000
% 14.77/15.20 maxlength = 115
% 14.77/15.20 maxnrvars = 195
% 14.77/15.20 excuselevel = 1
% 14.77/15.20 increasemaxweight = 1
% 14.77/15.20
% 14.77/15.20 maxselected = 10000000
% 14.77/15.20 maxnrclauses = 10000000
% 14.77/15.20
% 14.77/15.20 showgenerated = 0
% 14.77/15.20 showkept = 0
% 14.77/15.20 showselected = 0
% 14.77/15.20 showdeleted = 0
% 14.77/15.20 showresimp = 1
% 14.77/15.20 showstatus = 2000
% 14.77/15.20
% 14.77/15.20 prologoutput = 0
% 14.77/15.20 nrgoals = 5000000
% 14.77/15.20 totalproof = 1
% 14.77/15.20
% 14.77/15.20 Symbols occurring in the translation:
% 14.77/15.20
% 14.77/15.20 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 14.77/15.20 . [1, 2] (w:1, o:23, a:1, s:1, b:0),
% 14.77/15.20 ! [4, 1] (w:0, o:18, a:1, s:1, b:0),
% 14.77/15.20 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 14.77/15.20 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 14.77/15.20 distinct_points [36, 2] (w:1, o:48, a:1, s:1, b:0),
% 14.77/15.20 distinct_lines [37, 2] (w:1, o:49, a:1, s:1, b:0),
% 14.77/15.20 convergent_lines [38, 2] (w:1, o:47, a:1, s:1, b:0),
% 14.77/15.20 line_connecting [41, 2] (w:1, o:50, a:1, s:1, b:0),
% 14.77/15.20 apart_point_and_line [42, 2] (w:1, o:51, a:1, s:1, b:0),
% 14.77/15.20 intersection_point [43, 2] (w:1, o:52, a:1, s:1, b:0),
% 14.77/15.20 parallel_through_point [46, 2] (w:1, o:54, a:1, s:1, b:0),
% 14.77/15.20 unorthogonal_lines [49, 2] (w:1, o:55, a:1, s:1, b:0),
% 14.77/15.20 orthogonal_through_point [52, 2] (w:1, o:53, a:1, s:1, b:0),
% 14.77/15.20 alpha1 [53, 2] (w:1, o:56, a:1, s:1, b:0),
% 14.77/15.20 skol1 [54, 0] (w:1, o:15, a:1, s:1, b:0),
% 14.77/15.20 skol2 [55, 0] (w:1, o:16, a:1, s:1, b:0),
% 14.77/15.20 skol3 [56, 0] (w:1, o:17, a:1, s:1, b:0).
% 14.77/15.20
% 14.77/15.20
% 14.77/15.20 Starting Search:
% 14.77/15.20
% 14.77/15.20 *** allocated 15000 integers for clauses
% 14.77/15.20 *** allocated 22500 integers for clauses
% 14.77/15.20 *** allocated 33750 integers for clauses
% 14.77/15.20 *** allocated 15000 integers for termspace/termends
% 14.77/15.20 *** allocated 50625 integers for clauses
% 14.77/15.20 Resimplifying inuse:
% 14.77/15.20 Done
% 14.77/15.20
% 14.77/15.20 *** allocated 22500 integers for termspace/termends
% 14.77/15.20 *** allocated 75937 integers for clauses
% 14.77/15.20 *** allocated 33750 integers for termspace/termends
% 14.77/15.20 *** allocated 113905 integers for clauses
% 14.77/15.20
% 14.77/15.20 Intermediate Status:
% 14.77/15.20 Generated: 14795
% 14.77/15.20 Kept: 2009
% 14.77/15.20 Inuse: 304
% 14.77/15.20 Deleted: 0
% 14.77/15.20 Deletedinuse: 0
% 14.77/15.20
% 14.77/15.20 Resimplifying inuse:
% 14.77/15.20 Done
% 14.77/15.20
% 14.77/15.20 *** allocated 50625 integers for termspace/termends
% 14.77/15.20 *** allocated 170857 integers for clauses
% 14.77/15.20 Resimplifying inuse:
% 14.77/15.20 Done
% 14.77/15.20
% 14.77/15.20 *** allocated 75937 integers for termspace/termends
% 14.77/15.20
% 14.77/15.20 Intermediate Status:
% 14.77/15.20 Generated: 63167
% 14.77/15.20 Kept: 4009
% 14.77/15.20 Inuse: 656
% 14.77/15.20 Deleted: 7
% 14.77/15.20 Deletedinuse: 0
% 14.77/15.20
% 14.77/15.20 Resimplifying inuse:
% 14.77/15.20 Done
% 14.77/15.20
% 14.77/15.20 *** allocated 256285 integers for clauses
% 14.77/15.20 Resimplifying inuse:
% 14.77/15.20 Done
% 14.77/15.20
% 14.77/15.20 *** allocated 113905 integers for termspace/termends
% 14.77/15.20
% 14.77/15.20 Intermediate Status:
% 14.77/15.20 Generated: 534872
% 14.77/15.20 Kept: 6114
% 14.77/15.20 Inuse: 1663
% 14.77/15.20 Deleted: 80
% 14.77/15.20 Deletedinuse: 13
% 14.77/15.20
% 14.77/15.20 Resimplifying inuse:
% 14.77/15.20 Done
% 14.77/15.20
% 14.77/15.20 *** allocated 384427 integers for clauses
% 14.77/15.20 Resimplifying inuse:
% 14.77/15.20 Done
% 14.77/15.20
% 14.77/15.20 *** allocated 170857 integers for termspace/termends
% 14.77/15.20
% 14.77/15.20 Intermediate Status:
% 14.77/15.20 Generated: 592732
% 14.77/15.20 Kept: 8119
% 14.77/15.20 Inuse: 1724
% 14.77/15.20 Deleted: 82
% 14.77/15.20 Deletedinuse: 13
% 14.77/15.20
% 14.77/15.20 Resimplifying inuse:
% 14.77/15.20 Done
% 14.77/15.20
% 14.77/15.20 *** allocated 576640 integers for clauses
% 14.77/15.20 Resimplifying inuse:
% 14.77/15.20 Done
% 14.77/15.20
% 14.77/15.20
% 14.77/15.20 Intermediate Status:
% 14.77/15.20 Generated: 1001237
% 14.77/15.20 Kept: 10135
% 14.77/15.20 Inuse: 2214
% 14.77/15.20 Deleted: 122
% 14.77/15.20 Deletedinuse: 13
% 14.77/15.20
% 14.77/15.20 Resimplifying inuse:
% 14.77/15.20 Done
% 14.77/15.20
% 14.77/15.20
% 14.77/15.20 Bliksems!, er is een bewijs:
% 14.77/15.20 % SZS status Theorem
% 14.77/15.20 % SZS output start Refutation
% 14.77/15.20
% 14.77/15.20 (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 14.77/15.20 (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ), distinct_lines( Y, Z )
% 14.77/15.20 , ! distinct_lines( X, Y ) }.
% 14.77/15.20 (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ), apart_point_and_line(
% 14.77/15.20 X, Z ), ! apart_point_and_line( X, Y ) }.
% 14.77/15.20 (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( orthogonal_through_point
% 14.77/15.20 ( Y, X ), Y ) }.
% 14.77/15.20 (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 14.77/15.20 orthogonal_through_point( Y, X ) ) }.
% 14.77/15.20 (25) {G0,W15,D2,L5,V4,M2} I { ! distinct_lines( X, Y ),
% 14.77/15.20 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 14.77/15.20 unorthogonal_lines( Y, T ), unorthogonal_lines( X, T ) }.
% 14.77/15.20 (26) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol1, skol2 ) }.
% 14.77/15.20 (27) {G0,W3,D2,L1,V0,M1} I { ! unorthogonal_lines( skol2, skol3 ) }.
% 14.77/15.20 (28) {G0,W5,D3,L1,V0,M1} I { distinct_lines( skol2,
% 14.77/15.20 orthogonal_through_point( skol3, skol1 ) ) }.
% 14.77/15.20 (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ), distinct_lines
% 14.77/15.20 ( X, Y ) }.
% 14.77/15.20 (36) {G2,W5,D3,L1,V0,M1} R(34,28) { distinct_lines(
% 14.77/15.20 orthogonal_through_point( skol3, skol1 ), skol2 ) }.
% 14.77/15.20 (130) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ),
% 14.77/15.20 distinct_lines( Y, T ), apart_point_and_line( Z, T ), !
% 14.77/15.20 apart_point_and_line( Z, X ) }.
% 14.77/15.20 (145) {G1,W6,D2,L2,V1,M1} R(12,26) { distinct_lines( X, skol2 ), !
% 14.77/15.20 apart_point_and_line( skol1, X ) }.
% 14.77/15.20 (146) {G2,W9,D2,L3,V2,M1} R(145,12) { distinct_lines( X, skol2 ),
% 14.77/15.20 distinct_lines( Y, X ), ! apart_point_and_line( skol1, Y ) }.
% 14.77/15.20 (302) {G1,W16,D3,L4,V4,M1} R(25,23) { ! distinct_lines(
% 14.77/15.20 orthogonal_through_point( X, Y ), Z ), apart_point_and_line( T,
% 14.77/15.20 orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ),
% 14.77/15.20 unorthogonal_lines( Z, X ) }.
% 14.77/15.20 (3086) {G3,W15,D2,L5,V4,M1} R(130,146) { distinct_lines( X, Y ),
% 14.77/15.20 distinct_lines( Y, Z ), distinct_lines( T, skol2 ), distinct_lines( Z, T
% 14.77/15.20 ), ! apart_point_and_line( skol1, X ) }.
% 14.77/15.20 (3100) {G4,W9,D2,L3,V2,M1} F(3086);r(34) { distinct_lines( Y, X ),
% 14.77/15.20 distinct_lines( Y, skol2 ), ! apart_point_and_line( skol1, X ) }.
% 14.77/15.20 (3735) {G2,W13,D3,L3,V2,M1} R(302,27) { ! distinct_lines(
% 14.77/15.20 orthogonal_through_point( skol3, X ), skol2 ), apart_point_and_line( Y,
% 14.77/15.20 skol2 ), apart_point_and_line( Y, orthogonal_through_point( skol3, X ) )
% 14.77/15.20 }.
% 14.77/15.20 (10866) {G3,W8,D3,L2,V1,M1} R(3735,24) { ! distinct_lines(
% 14.77/15.20 orthogonal_through_point( skol3, X ), skol2 ), apart_point_and_line( X,
% 14.77/15.20 skol2 ) }.
% 14.77/15.20 (10917) {G5,W3,D2,L1,V1,M1} R(10866,3100);f;r(36) { distinct_lines( X,
% 14.77/15.20 skol2 ) }.
% 14.77/15.20 (10935) {G6,W0,D0,L0,V0,M0} R(10866,26);r(10917) { }.
% 14.77/15.20
% 14.77/15.20
% 14.77/15.20 % SZS output end Refutation
% 14.77/15.20 found a proof!
% 14.77/15.20
% 14.77/15.20
% 14.77/15.20 Unprocessed initial clauses:
% 14.77/15.20
% 14.77/15.20 (10937) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 14.77/15.20 (10938) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 14.77/15.20 (10939) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 14.77/15.20 (10940) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points(
% 14.77/15.20 X, Z ), distinct_points( Y, Z ) }.
% 14.77/15.20 (10941) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X
% 14.86/15.20 , Z ), distinct_lines( Y, Z ) }.
% 14.86/15.20 (10942) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines
% 14.86/15.20 ( X, Z ), convergent_lines( Y, Z ) }.
% 14.86/15.20 (10943) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 14.86/15.20 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 14.86/15.20 (10944) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 14.86/15.20 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 14.86/15.20 (10945) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 14.86/15.20 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 14.86/15.20 (10946) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 14.86/15.20 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 14.86/15.20 (10947) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines
% 14.86/15.20 ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 14.86/15.20 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 14.86/15.20 (10948) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 14.86/15.20 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 14.86/15.20 (10949) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 14.86/15.20 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 14.86/15.20 (10950) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), distinct_lines(
% 14.86/15.20 Y, Z ), convergent_lines( X, Z ) }.
% 14.86/15.20 (10951) {G0,W5,D3,L1,V2,M1} { ! convergent_lines( parallel_through_point(
% 14.86/15.20 Y, X ), Y ) }.
% 14.86/15.20 (10952) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 14.86/15.20 parallel_through_point( Y, X ) ) }.
% 14.86/15.20 (10953) {G0,W12,D2,L4,V3,M4} { ! distinct_lines( X, Y ),
% 14.86/15.20 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 14.86/15.20 convergent_lines( X, Y ) }.
% 14.86/15.20 (10954) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines
% 14.86/15.20 ( X, Y ) }.
% 14.86/15.20 (10955) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 14.86/15.20 unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 14.86/15.20 (10956) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 14.86/15.20 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 14.86/15.20 }.
% 14.86/15.20 (10957) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines( X, Y )
% 14.86/15.20 }.
% 14.86/15.20 (10958) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 14.86/15.20 }.
% 14.86/15.20 (10959) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( X, Y ), !
% 14.86/15.20 unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 14.86/15.20 (10960) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines(
% 14.86/15.20 orthogonal_through_point( Y, X ), Y ) }.
% 14.86/15.20 (10961) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 14.86/15.20 orthogonal_through_point( Y, X ) ) }.
% 14.86/15.20 (10962) {G0,W15,D2,L5,V4,M5} { ! distinct_lines( X, Y ),
% 14.86/15.20 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 14.86/15.20 unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 14.86/15.20 (10963) {G0,W3,D2,L1,V0,M1} { ! apart_point_and_line( skol1, skol2 ) }.
% 14.86/15.20 (10964) {G0,W3,D2,L1,V0,M1} { ! unorthogonal_lines( skol2, skol3 ) }.
% 14.86/15.20 (10965) {G0,W5,D3,L1,V0,M1} { distinct_lines( skol2,
% 14.86/15.20 orthogonal_through_point( skol3, skol1 ) ) }.
% 14.86/15.20
% 14.86/15.20
% 14.86/15.20 Total Proof:
% 14.86/15.20
% 14.86/15.20 subsumption: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 14.86/15.20 parent0: (10938) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 14.86/15.20 substitution0:
% 14.86/15.20 X := X
% 14.86/15.20 end
% 14.86/15.20 permutation0:
% 14.86/15.20 0 ==> 0
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 subsumption: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 14.86/15.20 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 14.86/15.20 parent0: (10941) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ),
% 14.86/15.20 distinct_lines( X, Z ), distinct_lines( Y, Z ) }.
% 14.86/15.20 substitution0:
% 14.86/15.20 X := X
% 14.86/15.20 Y := Y
% 14.86/15.20 Z := Z
% 14.86/15.20 end
% 14.86/15.20 permutation0:
% 14.86/15.20 0 ==> 2
% 14.86/15.20 1 ==> 0
% 14.86/15.20 2 ==> 1
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 subsumption: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 14.86/15.20 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 14.86/15.20 parent0: (10949) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 14.86/15.20 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 14.86/15.20 substitution0:
% 14.86/15.20 X := X
% 14.86/15.20 Y := Y
% 14.86/15.20 Z := Z
% 14.86/15.20 end
% 14.86/15.20 permutation0:
% 14.86/15.20 0 ==> 2
% 14.86/15.20 1 ==> 0
% 14.86/15.20 2 ==> 1
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 subsumption: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 14.86/15.20 orthogonal_through_point( Y, X ), Y ) }.
% 14.86/15.20 parent0: (10960) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines(
% 14.86/15.20 orthogonal_through_point( Y, X ), Y ) }.
% 14.86/15.20 substitution0:
% 14.86/15.20 X := X
% 14.86/15.20 Y := Y
% 14.86/15.20 end
% 14.86/15.20 permutation0:
% 14.86/15.20 0 ==> 0
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 subsumption: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 14.86/15.20 orthogonal_through_point( Y, X ) ) }.
% 14.86/15.20 parent0: (10961) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 14.86/15.20 orthogonal_through_point( Y, X ) ) }.
% 14.86/15.20 substitution0:
% 14.86/15.20 X := X
% 14.86/15.20 Y := Y
% 14.86/15.20 end
% 14.86/15.20 permutation0:
% 14.86/15.20 0 ==> 0
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 subsumption: (25) {G0,W15,D2,L5,V4,M2} I { ! distinct_lines( X, Y ),
% 14.86/15.20 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 14.86/15.20 unorthogonal_lines( Y, T ), unorthogonal_lines( X, T ) }.
% 14.86/15.20 parent0: (10962) {G0,W15,D2,L5,V4,M5} { ! distinct_lines( X, Y ),
% 14.86/15.20 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 14.86/15.20 unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 14.86/15.20 substitution0:
% 14.86/15.20 X := X
% 14.86/15.20 Y := Y
% 14.86/15.20 Z := Z
% 14.86/15.20 T := T
% 14.86/15.20 end
% 14.86/15.20 permutation0:
% 14.86/15.20 0 ==> 0
% 14.86/15.20 1 ==> 1
% 14.86/15.20 2 ==> 2
% 14.86/15.20 3 ==> 4
% 14.86/15.20 4 ==> 3
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 subsumption: (26) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol1,
% 14.86/15.20 skol2 ) }.
% 14.86/15.20 parent0: (10963) {G0,W3,D2,L1,V0,M1} { ! apart_point_and_line( skol1,
% 14.86/15.20 skol2 ) }.
% 14.86/15.20 substitution0:
% 14.86/15.20 end
% 14.86/15.20 permutation0:
% 14.86/15.20 0 ==> 0
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 subsumption: (27) {G0,W3,D2,L1,V0,M1} I { ! unorthogonal_lines( skol2,
% 14.86/15.20 skol3 ) }.
% 14.86/15.20 parent0: (10964) {G0,W3,D2,L1,V0,M1} { ! unorthogonal_lines( skol2, skol3
% 14.86/15.20 ) }.
% 14.86/15.20 substitution0:
% 14.86/15.20 end
% 14.86/15.20 permutation0:
% 14.86/15.20 0 ==> 0
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 subsumption: (28) {G0,W5,D3,L1,V0,M1} I { distinct_lines( skol2,
% 14.86/15.20 orthogonal_through_point( skol3, skol1 ) ) }.
% 14.86/15.20 parent0: (10965) {G0,W5,D3,L1,V0,M1} { distinct_lines( skol2,
% 14.86/15.20 orthogonal_through_point( skol3, skol1 ) ) }.
% 14.86/15.20 substitution0:
% 14.86/15.20 end
% 14.86/15.20 permutation0:
% 14.86/15.20 0 ==> 0
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 resolution: (11045) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 14.86/15.20 distinct_lines( X, Y ) }.
% 14.86/15.20 parent0[0]: (1) {G0,W3,D2,L1,V1,M1} I { ! distinct_lines( X, X ) }.
% 14.86/15.20 parent1[0]: (4) {G0,W9,D2,L3,V3,M3} I { distinct_lines( X, Z ),
% 14.86/15.20 distinct_lines( Y, Z ), ! distinct_lines( X, Y ) }.
% 14.86/15.20 substitution0:
% 14.86/15.20 X := X
% 14.86/15.20 end
% 14.86/15.20 substitution1:
% 14.86/15.20 X := X
% 14.86/15.20 Y := Y
% 14.86/15.20 Z := X
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 subsumption: (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 14.86/15.20 distinct_lines( X, Y ) }.
% 14.86/15.20 parent0: (11045) {G1,W6,D2,L2,V2,M2} { distinct_lines( Y, X ), !
% 14.86/15.20 distinct_lines( X, Y ) }.
% 14.86/15.20 substitution0:
% 14.86/15.20 X := Y
% 14.86/15.20 Y := X
% 14.86/15.20 end
% 14.86/15.20 permutation0:
% 14.86/15.20 0 ==> 1
% 14.86/15.20 1 ==> 0
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 resolution: (11047) {G1,W5,D3,L1,V0,M1} { distinct_lines(
% 14.86/15.20 orthogonal_through_point( skol3, skol1 ), skol2 ) }.
% 14.86/15.20 parent0[0]: (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 14.86/15.20 distinct_lines( X, Y ) }.
% 14.86/15.20 parent1[0]: (28) {G0,W5,D3,L1,V0,M1} I { distinct_lines( skol2,
% 14.86/15.20 orthogonal_through_point( skol3, skol1 ) ) }.
% 14.86/15.20 substitution0:
% 14.86/15.20 X := orthogonal_through_point( skol3, skol1 )
% 14.86/15.20 Y := skol2
% 14.86/15.20 end
% 14.86/15.20 substitution1:
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 subsumption: (36) {G2,W5,D3,L1,V0,M1} R(34,28) { distinct_lines(
% 14.86/15.20 orthogonal_through_point( skol3, skol1 ), skol2 ) }.
% 14.86/15.20 parent0: (11047) {G1,W5,D3,L1,V0,M1} { distinct_lines(
% 14.86/15.20 orthogonal_through_point( skol3, skol1 ), skol2 ) }.
% 14.86/15.20 substitution0:
% 14.86/15.20 end
% 14.86/15.20 permutation0:
% 14.86/15.20 0 ==> 0
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 resolution: (11048) {G1,W12,D2,L4,V4,M4} { distinct_lines( X, Y ),
% 14.86/15.20 apart_point_and_line( Z, Y ), distinct_lines( T, X ), !
% 14.86/15.20 apart_point_and_line( Z, T ) }.
% 14.86/15.20 parent0[2]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 14.86/15.20 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 14.86/15.20 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 14.86/15.20 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 14.86/15.20 substitution0:
% 14.86/15.20 X := Z
% 14.86/15.20 Y := X
% 14.86/15.20 Z := Y
% 14.86/15.20 end
% 14.86/15.20 substitution1:
% 14.86/15.20 X := Z
% 14.86/15.20 Y := T
% 14.86/15.20 Z := X
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 subsumption: (130) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ),
% 14.86/15.20 distinct_lines( Y, T ), apart_point_and_line( Z, T ), !
% 14.86/15.20 apart_point_and_line( Z, X ) }.
% 14.86/15.20 parent0: (11048) {G1,W12,D2,L4,V4,M4} { distinct_lines( X, Y ),
% 14.86/15.20 apart_point_and_line( Z, Y ), distinct_lines( T, X ), !
% 14.86/15.20 apart_point_and_line( Z, T ) }.
% 14.86/15.20 substitution0:
% 14.86/15.20 X := Y
% 14.86/15.20 Y := T
% 14.86/15.20 Z := Z
% 14.86/15.20 T := X
% 14.86/15.20 end
% 14.86/15.20 permutation0:
% 14.86/15.20 0 ==> 1
% 14.86/15.20 1 ==> 2
% 14.86/15.20 2 ==> 0
% 14.86/15.20 3 ==> 3
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 resolution: (11050) {G1,W6,D2,L2,V1,M2} { distinct_lines( X, skol2 ), !
% 14.86/15.20 apart_point_and_line( skol1, X ) }.
% 14.86/15.20 parent0[0]: (26) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol1,
% 14.86/15.20 skol2 ) }.
% 14.86/15.20 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 14.86/15.20 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 14.86/15.20 substitution0:
% 14.86/15.20 end
% 14.86/15.20 substitution1:
% 14.86/15.20 X := skol1
% 14.86/15.20 Y := X
% 14.86/15.20 Z := skol2
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 subsumption: (145) {G1,W6,D2,L2,V1,M1} R(12,26) { distinct_lines( X, skol2
% 14.86/15.20 ), ! apart_point_and_line( skol1, X ) }.
% 14.86/15.20 parent0: (11050) {G1,W6,D2,L2,V1,M2} { distinct_lines( X, skol2 ), !
% 14.86/15.20 apart_point_and_line( skol1, X ) }.
% 14.86/15.20 substitution0:
% 14.86/15.20 X := X
% 14.86/15.20 end
% 14.86/15.20 permutation0:
% 14.86/15.20 0 ==> 0
% 14.86/15.20 1 ==> 1
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 resolution: (11051) {G1,W9,D2,L3,V2,M3} { distinct_lines( X, skol2 ),
% 14.86/15.20 distinct_lines( Y, X ), ! apart_point_and_line( skol1, Y ) }.
% 14.86/15.20 parent0[1]: (145) {G1,W6,D2,L2,V1,M1} R(12,26) { distinct_lines( X, skol2 )
% 14.86/15.20 , ! apart_point_and_line( skol1, X ) }.
% 14.86/15.20 parent1[1]: (12) {G0,W9,D2,L3,V3,M2} I { distinct_lines( Y, Z ),
% 14.86/15.20 apart_point_and_line( X, Z ), ! apart_point_and_line( X, Y ) }.
% 14.86/15.20 substitution0:
% 14.86/15.20 X := X
% 14.86/15.20 end
% 14.86/15.20 substitution1:
% 14.86/15.20 X := skol1
% 14.86/15.20 Y := Y
% 14.86/15.20 Z := X
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 subsumption: (146) {G2,W9,D2,L3,V2,M1} R(145,12) { distinct_lines( X, skol2
% 14.86/15.20 ), distinct_lines( Y, X ), ! apart_point_and_line( skol1, Y ) }.
% 14.86/15.20 parent0: (11051) {G1,W9,D2,L3,V2,M3} { distinct_lines( X, skol2 ),
% 14.86/15.20 distinct_lines( Y, X ), ! apart_point_and_line( skol1, Y ) }.
% 14.86/15.20 substitution0:
% 14.86/15.20 X := X
% 14.86/15.20 Y := Y
% 14.86/15.20 end
% 14.86/15.20 permutation0:
% 14.86/15.20 0 ==> 0
% 14.86/15.20 1 ==> 1
% 14.86/15.20 2 ==> 2
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 resolution: (11054) {G1,W16,D3,L4,V4,M4} { ! distinct_lines(
% 14.86/15.20 orthogonal_through_point( X, Y ), Z ), apart_point_and_line( T,
% 14.86/15.20 orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ),
% 14.86/15.20 unorthogonal_lines( Z, X ) }.
% 14.86/15.20 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 14.86/15.20 orthogonal_through_point( Y, X ), Y ) }.
% 14.86/15.20 parent1[4]: (25) {G0,W15,D2,L5,V4,M2} I { ! distinct_lines( X, Y ),
% 14.86/15.20 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 14.86/15.20 unorthogonal_lines( Y, T ), unorthogonal_lines( X, T ) }.
% 14.86/15.20 substitution0:
% 14.86/15.20 X := Y
% 14.86/15.20 Y := X
% 14.86/15.20 end
% 14.86/15.20 substitution1:
% 14.86/15.20 X := orthogonal_through_point( X, Y )
% 14.86/15.20 Y := Z
% 14.86/15.20 Z := T
% 14.86/15.20 T := X
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 subsumption: (302) {G1,W16,D3,L4,V4,M1} R(25,23) { ! distinct_lines(
% 14.86/15.20 orthogonal_through_point( X, Y ), Z ), apart_point_and_line( T,
% 14.86/15.20 orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ),
% 14.86/15.20 unorthogonal_lines( Z, X ) }.
% 14.86/15.20 parent0: (11054) {G1,W16,D3,L4,V4,M4} { ! distinct_lines(
% 14.86/15.20 orthogonal_through_point( X, Y ), Z ), apart_point_and_line( T,
% 14.86/15.20 orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ),
% 14.86/15.20 unorthogonal_lines( Z, X ) }.
% 14.86/15.20 substitution0:
% 14.86/15.20 X := X
% 14.86/15.20 Y := Y
% 14.86/15.20 Z := Z
% 14.86/15.20 T := T
% 14.86/15.20 end
% 14.86/15.20 permutation0:
% 14.86/15.20 0 ==> 0
% 14.86/15.20 1 ==> 1
% 14.86/15.20 2 ==> 2
% 14.86/15.20 3 ==> 3
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 resolution: (11056) {G2,W15,D2,L5,V4,M5} { distinct_lines( X, skol2 ),
% 14.86/15.20 distinct_lines( Y, X ), distinct_lines( Z, T ), distinct_lines( T, Y ), !
% 14.86/15.20 apart_point_and_line( skol1, Z ) }.
% 14.86/15.20 parent0[2]: (146) {G2,W9,D2,L3,V2,M1} R(145,12) { distinct_lines( X, skol2
% 14.86/15.20 ), distinct_lines( Y, X ), ! apart_point_and_line( skol1, Y ) }.
% 14.86/15.20 parent1[2]: (130) {G1,W12,D2,L4,V4,M2} R(12,12) { distinct_lines( X, Y ),
% 14.86/15.20 distinct_lines( Y, T ), apart_point_and_line( Z, T ), !
% 14.86/15.20 apart_point_and_line( Z, X ) }.
% 14.86/15.20 substitution0:
% 14.86/15.20 X := X
% 14.86/15.20 Y := Y
% 14.86/15.20 end
% 14.86/15.20 substitution1:
% 14.86/15.20 X := Z
% 14.86/15.20 Y := T
% 14.86/15.20 Z := skol1
% 14.86/15.20 T := Y
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 subsumption: (3086) {G3,W15,D2,L5,V4,M1} R(130,146) { distinct_lines( X, Y
% 14.86/15.20 ), distinct_lines( Y, Z ), distinct_lines( T, skol2 ), distinct_lines( Z
% 14.86/15.20 , T ), ! apart_point_and_line( skol1, X ) }.
% 14.86/15.20 parent0: (11056) {G2,W15,D2,L5,V4,M5} { distinct_lines( X, skol2 ),
% 14.86/15.20 distinct_lines( Y, X ), distinct_lines( Z, T ), distinct_lines( T, Y ), !
% 14.86/15.20 apart_point_and_line( skol1, Z ) }.
% 14.86/15.20 substitution0:
% 14.86/15.20 X := T
% 14.86/15.20 Y := Z
% 14.86/15.20 Z := X
% 14.86/15.20 T := Y
% 14.86/15.20 end
% 14.86/15.20 permutation0:
% 14.86/15.20 0 ==> 2
% 14.86/15.20 1 ==> 3
% 14.86/15.20 2 ==> 0
% 14.86/15.20 3 ==> 1
% 14.86/15.20 4 ==> 4
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 factor: (11070) {G3,W12,D2,L4,V2,M4} { distinct_lines( X, Y ),
% 14.86/15.20 distinct_lines( Y, X ), distinct_lines( Y, skol2 ), !
% 14.86/15.20 apart_point_and_line( skol1, X ) }.
% 14.86/15.20 parent0[0, 3]: (3086) {G3,W15,D2,L5,V4,M1} R(130,146) { distinct_lines( X,
% 14.86/15.20 Y ), distinct_lines( Y, Z ), distinct_lines( T, skol2 ), distinct_lines(
% 14.86/15.20 Z, T ), ! apart_point_and_line( skol1, X ) }.
% 14.86/15.20 substitution0:
% 14.86/15.20 X := X
% 14.86/15.20 Y := Y
% 14.86/15.20 Z := X
% 14.86/15.20 T := Y
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 resolution: (11094) {G2,W12,D2,L4,V2,M4} { distinct_lines( Y, X ),
% 14.86/15.20 distinct_lines( Y, X ), distinct_lines( Y, skol2 ), !
% 14.86/15.20 apart_point_and_line( skol1, X ) }.
% 14.86/15.20 parent0[0]: (34) {G1,W6,D2,L2,V2,M2} R(4,1) { ! distinct_lines( Y, X ),
% 14.86/15.20 distinct_lines( X, Y ) }.
% 14.86/15.20 parent1[0]: (11070) {G3,W12,D2,L4,V2,M4} { distinct_lines( X, Y ),
% 14.86/15.20 distinct_lines( Y, X ), distinct_lines( Y, skol2 ), !
% 14.86/15.20 apart_point_and_line( skol1, X ) }.
% 14.86/15.20 substitution0:
% 14.86/15.20 X := Y
% 14.86/15.20 Y := X
% 14.86/15.20 end
% 14.86/15.20 substitution1:
% 14.86/15.20 X := X
% 14.86/15.20 Y := Y
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 factor: (11097) {G2,W9,D2,L3,V2,M3} { distinct_lines( X, Y ),
% 14.86/15.20 distinct_lines( X, skol2 ), ! apart_point_and_line( skol1, Y ) }.
% 14.86/15.20 parent0[0, 1]: (11094) {G2,W12,D2,L4,V2,M4} { distinct_lines( Y, X ),
% 14.86/15.20 distinct_lines( Y, X ), distinct_lines( Y, skol2 ), !
% 14.86/15.20 apart_point_and_line( skol1, X ) }.
% 14.86/15.20 substitution0:
% 14.86/15.20 X := Y
% 14.86/15.20 Y := X
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 subsumption: (3100) {G4,W9,D2,L3,V2,M1} F(3086);r(34) { distinct_lines( Y,
% 14.86/15.20 X ), distinct_lines( Y, skol2 ), ! apart_point_and_line( skol1, X ) }.
% 14.86/15.20 parent0: (11097) {G2,W9,D2,L3,V2,M3} { distinct_lines( X, Y ),
% 14.86/15.20 distinct_lines( X, skol2 ), ! apart_point_and_line( skol1, Y ) }.
% 14.86/15.20 substitution0:
% 14.86/15.20 X := Y
% 14.86/15.20 Y := X
% 14.86/15.20 end
% 14.86/15.20 permutation0:
% 14.86/15.20 0 ==> 0
% 14.86/15.20 1 ==> 1
% 14.86/15.20 2 ==> 2
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 resolution: (11101) {G1,W13,D3,L3,V2,M3} { ! distinct_lines(
% 14.86/15.20 orthogonal_through_point( skol3, X ), skol2 ), apart_point_and_line( Y,
% 14.86/15.20 orthogonal_through_point( skol3, X ) ), apart_point_and_line( Y, skol2 )
% 14.86/15.20 }.
% 14.86/15.20 parent0[0]: (27) {G0,W3,D2,L1,V0,M1} I { ! unorthogonal_lines( skol2, skol3
% 14.86/15.20 ) }.
% 14.86/15.20 parent1[3]: (302) {G1,W16,D3,L4,V4,M1} R(25,23) { ! distinct_lines(
% 14.86/15.20 orthogonal_through_point( X, Y ), Z ), apart_point_and_line( T,
% 14.86/15.20 orthogonal_through_point( X, Y ) ), apart_point_and_line( T, Z ),
% 14.86/15.20 unorthogonal_lines( Z, X ) }.
% 14.86/15.20 substitution0:
% 14.86/15.20 end
% 14.86/15.20 substitution1:
% 14.86/15.20 X := skol3
% 14.86/15.20 Y := X
% 14.86/15.20 Z := skol2
% 14.86/15.20 T := Y
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 subsumption: (3735) {G2,W13,D3,L3,V2,M1} R(302,27) { ! distinct_lines(
% 14.86/15.20 orthogonal_through_point( skol3, X ), skol2 ), apart_point_and_line( Y,
% 14.86/15.20 skol2 ), apart_point_and_line( Y, orthogonal_through_point( skol3, X ) )
% 14.86/15.20 }.
% 14.86/15.20 parent0: (11101) {G1,W13,D3,L3,V2,M3} { ! distinct_lines(
% 14.86/15.20 orthogonal_through_point( skol3, X ), skol2 ), apart_point_and_line( Y,
% 14.86/15.20 orthogonal_through_point( skol3, X ) ), apart_point_and_line( Y, skol2 )
% 14.86/15.20 }.
% 14.86/15.20 substitution0:
% 14.86/15.20 X := X
% 14.86/15.20 Y := Y
% 14.86/15.20 end
% 14.86/15.20 permutation0:
% 14.86/15.20 0 ==> 0
% 14.86/15.20 1 ==> 2
% 14.86/15.20 2 ==> 1
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 resolution: (11102) {G1,W8,D3,L2,V1,M2} { ! distinct_lines(
% 14.86/15.20 orthogonal_through_point( skol3, X ), skol2 ), apart_point_and_line( X,
% 14.86/15.20 skol2 ) }.
% 14.86/15.20 parent0[0]: (24) {G0,W5,D3,L1,V2,M1} I { ! apart_point_and_line( X,
% 14.86/15.20 orthogonal_through_point( Y, X ) ) }.
% 14.86/15.20 parent1[2]: (3735) {G2,W13,D3,L3,V2,M1} R(302,27) { ! distinct_lines(
% 14.86/15.20 orthogonal_through_point( skol3, X ), skol2 ), apart_point_and_line( Y,
% 14.86/15.20 skol2 ), apart_point_and_line( Y, orthogonal_through_point( skol3, X ) )
% 14.86/15.20 }.
% 14.86/15.20 substitution0:
% 14.86/15.20 X := X
% 14.86/15.20 Y := skol3
% 14.86/15.20 end
% 14.86/15.20 substitution1:
% 14.86/15.20 X := X
% 14.86/15.20 Y := X
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 subsumption: (10866) {G3,W8,D3,L2,V1,M1} R(3735,24) { ! distinct_lines(
% 14.86/15.20 orthogonal_through_point( skol3, X ), skol2 ), apart_point_and_line( X,
% 14.86/15.20 skol2 ) }.
% 14.86/15.20 parent0: (11102) {G1,W8,D3,L2,V1,M2} { ! distinct_lines(
% 14.86/15.20 orthogonal_through_point( skol3, X ), skol2 ), apart_point_and_line( X,
% 14.86/15.20 skol2 ) }.
% 14.86/15.20 substitution0:
% 14.86/15.20 X := X
% 14.86/15.20 end
% 14.86/15.20 permutation0:
% 14.86/15.20 0 ==> 0
% 14.86/15.20 1 ==> 1
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 resolution: (11105) {G4,W11,D3,L3,V1,M3} { distinct_lines( X, skol2 ),
% 14.86/15.20 distinct_lines( X, skol2 ), ! distinct_lines( orthogonal_through_point(
% 14.86/15.20 skol3, skol1 ), skol2 ) }.
% 14.86/15.20 parent0[2]: (3100) {G4,W9,D2,L3,V2,M1} F(3086);r(34) { distinct_lines( Y, X
% 14.86/15.20 ), distinct_lines( Y, skol2 ), ! apart_point_and_line( skol1, X ) }.
% 14.86/15.20 parent1[1]: (10866) {G3,W8,D3,L2,V1,M1} R(3735,24) { ! distinct_lines(
% 14.86/15.20 orthogonal_through_point( skol3, X ), skol2 ), apart_point_and_line( X,
% 14.86/15.20 skol2 ) }.
% 14.86/15.20 substitution0:
% 14.86/15.20 X := skol2
% 14.86/15.20 Y := X
% 14.86/15.20 end
% 14.86/15.20 substitution1:
% 14.86/15.20 X := skol1
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 resolution: (11107) {G3,W6,D2,L2,V1,M2} { distinct_lines( X, skol2 ),
% 14.86/15.20 distinct_lines( X, skol2 ) }.
% 14.86/15.20 parent0[2]: (11105) {G4,W11,D3,L3,V1,M3} { distinct_lines( X, skol2 ),
% 14.86/15.20 distinct_lines( X, skol2 ), ! distinct_lines( orthogonal_through_point(
% 14.86/15.20 skol3, skol1 ), skol2 ) }.
% 14.86/15.20 parent1[0]: (36) {G2,W5,D3,L1,V0,M1} R(34,28) { distinct_lines(
% 14.86/15.20 orthogonal_through_point( skol3, skol1 ), skol2 ) }.
% 14.86/15.20 substitution0:
% 14.86/15.20 X := X
% 14.86/15.20 end
% 14.86/15.20 substitution1:
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 factor: (11108) {G3,W3,D2,L1,V1,M1} { distinct_lines( X, skol2 ) }.
% 14.86/15.20 parent0[0, 1]: (11107) {G3,W6,D2,L2,V1,M2} { distinct_lines( X, skol2 ),
% 14.86/15.20 distinct_lines( X, skol2 ) }.
% 14.86/15.20 substitution0:
% 14.86/15.20 X := X
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 subsumption: (10917) {G5,W3,D2,L1,V1,M1} R(10866,3100);f;r(36) {
% 14.86/15.20 distinct_lines( X, skol2 ) }.
% 14.86/15.20 parent0: (11108) {G3,W3,D2,L1,V1,M1} { distinct_lines( X, skol2 ) }.
% 14.86/15.20 substitution0:
% 14.86/15.20 X := X
% 14.86/15.20 end
% 14.86/15.20 permutation0:
% 14.86/15.20 0 ==> 0
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 resolution: (11109) {G1,W5,D3,L1,V0,M1} { ! distinct_lines(
% 14.86/15.20 orthogonal_through_point( skol3, skol1 ), skol2 ) }.
% 14.86/15.20 parent0[0]: (26) {G0,W3,D2,L1,V0,M1} I { ! apart_point_and_line( skol1,
% 14.86/15.20 skol2 ) }.
% 14.86/15.20 parent1[1]: (10866) {G3,W8,D3,L2,V1,M1} R(3735,24) { ! distinct_lines(
% 14.86/15.20 orthogonal_through_point( skol3, X ), skol2 ), apart_point_and_line( X,
% 14.86/15.20 skol2 ) }.
% 14.86/15.20 substitution0:
% 14.86/15.20 end
% 14.86/15.20 substitution1:
% 14.86/15.20 X := skol1
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 resolution: (11110) {G2,W0,D0,L0,V0,M0} { }.
% 14.86/15.20 parent0[0]: (11109) {G1,W5,D3,L1,V0,M1} { ! distinct_lines(
% 14.86/15.20 orthogonal_through_point( skol3, skol1 ), skol2 ) }.
% 14.86/15.20 parent1[0]: (10917) {G5,W3,D2,L1,V1,M1} R(10866,3100);f;r(36) {
% 14.86/15.20 distinct_lines( X, skol2 ) }.
% 14.86/15.20 substitution0:
% 14.86/15.20 end
% 14.86/15.20 substitution1:
% 14.86/15.20 X := orthogonal_through_point( skol3, skol1 )
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 subsumption: (10935) {G6,W0,D0,L0,V0,M0} R(10866,26);r(10917) { }.
% 14.86/15.20 parent0: (11110) {G2,W0,D0,L0,V0,M0} { }.
% 14.86/15.20 substitution0:
% 14.86/15.20 end
% 14.86/15.20 permutation0:
% 14.86/15.20 end
% 14.86/15.20
% 14.86/15.20 Proof check complete!
% 14.86/15.20
% 14.86/15.20 Memory use:
% 14.86/15.20
% 14.86/15.20 space for terms: 159640
% 14.86/15.20 space for clauses: 461406
% 14.86/15.20
% 14.86/15.20
% 14.86/15.20 clauses generated: 1260822
% 14.86/15.20 clauses kept: 10936
% 14.86/15.20 clauses selected: 2754
% 14.86/15.20 clauses deleted: 126
% 14.86/15.20 clauses inuse deleted: 13
% 14.86/15.20
% 14.86/15.20 subsentry: 8901560
% 14.86/15.20 literals s-matched: 2700027
% 14.86/15.20 literals matched: 2699970
% 14.86/15.20 full subsumption: 1515057
% 14.86/15.20
% 14.86/15.20 checksum: -1019671627
% 14.86/15.20
% 14.86/15.20
% 14.86/15.20 Bliksem ended
%------------------------------------------------------------------------------