TSTP Solution File: GEO222+3 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GEO222+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n032.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 02:52:58 EDT 2022
% Result : Theorem 0.71s 1.14s
% Output : Refutation 0.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GEO222+3 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.10 % Command : bliksem %s
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % DateTime : Sat Jun 18 10:54:17 EDT 2022
% 0.09/0.28 % CPUTime :
% 0.71/1.14 *** allocated 10000 integers for termspace/termends
% 0.71/1.14 *** allocated 10000 integers for clauses
% 0.71/1.14 *** allocated 10000 integers for justifications
% 0.71/1.14 Bliksem 1.12
% 0.71/1.14
% 0.71/1.14
% 0.71/1.14 Automatic Strategy Selection
% 0.71/1.14
% 0.71/1.14
% 0.71/1.14 Clauses:
% 0.71/1.14
% 0.71/1.14 { ! distinct_points( X, X ) }.
% 0.71/1.14 { ! distinct_lines( X, X ) }.
% 0.71/1.14 { ! convergent_lines( X, X ) }.
% 0.71/1.14 { ! distinct_points( X, Y ), distinct_points( X, Z ), distinct_points( Y, Z
% 0.71/1.14 ) }.
% 0.71/1.14 { ! distinct_lines( X, Y ), distinct_lines( X, Z ), distinct_lines( Y, Z )
% 0.71/1.14 }.
% 0.71/1.14 { ! convergent_lines( X, Y ), convergent_lines( X, Z ), convergent_lines( Y
% 0.71/1.14 , Z ) }.
% 0.71/1.14 { ! distinct_points( X, Y ), ! apart_point_and_line( X, line_connecting( X
% 0.71/1.14 , Y ) ) }.
% 0.71/1.14 { ! distinct_points( X, Y ), ! apart_point_and_line( Y, line_connecting( X
% 0.71/1.14 , Y ) ) }.
% 0.71/1.14 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.71/1.14 , Y ), X ) }.
% 0.71/1.14 { ! convergent_lines( X, Y ), ! apart_point_and_line( intersection_point( X
% 0.71/1.14 , Y ), Y ) }.
% 0.71/1.14 { ! distinct_points( X, Y ), ! distinct_lines( Z, T ), apart_point_and_line
% 0.71/1.14 ( X, Z ), apart_point_and_line( X, T ), apart_point_and_line( Y, Z ),
% 0.71/1.14 apart_point_and_line( Y, T ) }.
% 0.71/1.14 { ! apart_point_and_line( X, Y ), distinct_points( X, Z ),
% 0.71/1.14 apart_point_and_line( Z, Y ) }.
% 0.71/1.14 { ! apart_point_and_line( X, Y ), distinct_lines( Y, Z ),
% 0.71/1.14 apart_point_and_line( X, Z ) }.
% 0.71/1.14 { ! convergent_lines( X, Y ), distinct_lines( Y, Z ), convergent_lines( X,
% 0.71/1.14 Z ) }.
% 0.71/1.14 { ! distinct_lines( X, Y ), convergent_lines( X, Y ) }.
% 0.71/1.14 { ! convergent_lines( parallel_through_point( Y, X ), Y ) }.
% 0.71/1.14 { ! apart_point_and_line( X, parallel_through_point( Y, X ) ) }.
% 0.71/1.14 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 0.71/1.14 apart_point_and_line( Z, Y ), convergent_lines( X, Y ) }.
% 0.71/1.14 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.71/1.14 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.71/1.14 , convergent_lines( Y, Z ) }.
% 0.71/1.14 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Z )
% 0.71/1.14 , unorthogonal_lines( Y, Z ) }.
% 0.71/1.14 { ! alpha1( X, Y ), convergent_lines( X, Y ) }.
% 0.71/1.14 { ! alpha1( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.71/1.14 { ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ), alpha1( X, Y )
% 0.71/1.14 }.
% 0.71/1.14 { ! unorthogonal_lines( orthogonal_through_point( Y, X ), Y ) }.
% 0.71/1.14 { ! apart_point_and_line( X, orthogonal_through_point( Y, X ) ) }.
% 0.71/1.14 { ! distinct_lines( X, Y ), apart_point_and_line( Z, X ),
% 0.71/1.14 apart_point_and_line( Z, Y ), unorthogonal_lines( X, T ),
% 0.71/1.14 unorthogonal_lines( Y, T ) }.
% 0.71/1.14 { convergent_lines( X, Y ), unorthogonal_lines( X, Y ) }.
% 0.71/1.14 { alpha2( X, Z ), convergent_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 0.71/1.14 unorthogonal_lines( X, Y ) }.
% 0.71/1.14 { alpha2( X, Z ), unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ), !
% 0.71/1.14 unorthogonal_lines( X, Y ) }.
% 0.71/1.14 { ! alpha2( X, Y ), convergent_lines( Y, X ) }.
% 0.71/1.14 { ! alpha2( X, Y ), unorthogonal_lines( Y, X ) }.
% 0.71/1.14 { ! convergent_lines( Y, X ), ! unorthogonal_lines( Y, X ), alpha2( X, Y )
% 0.71/1.14 }.
% 0.71/1.14 { unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ), !
% 0.71/1.14 convergent_lines( X, Y ) }.
% 0.71/1.14 { ! point( X ), ! point( Y ), ! distinct_points( X, Y ), line(
% 0.71/1.14 line_connecting( X, Y ) ) }.
% 0.71/1.14 { ! line( X ), ! line( Y ), ! convergent_lines( X, Y ), point(
% 0.71/1.14 intersection_point( X, Y ) ) }.
% 0.71/1.14 { ! line( X ), ! point( Y ), line( parallel_through_point( X, Y ) ) }.
% 0.71/1.14 { ! line( X ), ! point( Y ), line( orthogonal_through_point( X, Y ) ) }.
% 0.71/1.14 { ! equal_points( X, Y ), ! distinct_points( X, Y ) }.
% 0.71/1.14 { distinct_points( X, Y ), equal_points( X, Y ) }.
% 0.71/1.14 { ! equal_lines( X, Y ), ! distinct_lines( X, Y ) }.
% 0.71/1.14 { distinct_lines( X, Y ), equal_lines( X, Y ) }.
% 0.71/1.14 { ! parallel_lines( X, Y ), ! convergent_lines( X, Y ) }.
% 0.71/1.14 { convergent_lines( X, Y ), parallel_lines( X, Y ) }.
% 0.71/1.14 { ! incident_point_and_line( X, Y ), ! apart_point_and_line( X, Y ) }.
% 0.71/1.14 { apart_point_and_line( X, Y ), incident_point_and_line( X, Y ) }.
% 0.71/1.14 { ! orthogonal_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.71/1.14 { unorthogonal_lines( X, Y ), orthogonal_lines( X, Y ) }.
% 0.71/1.14 { ! parallel_lines( skol2, orthogonal_through_point(
% 0.71/1.14 orthogonal_through_point( skol2, skol1 ), skol1 ) ) }.
% 0.71/1.14
% 0.71/1.14 percentage equality = 0.000000, percentage horn = 0.595745
% 0.71/1.14 This a non-horn, non-equality problem
% 0.71/1.14
% 0.71/1.14
% 0.71/1.14 Options Used:
% 0.71/1.14
% 0.71/1.14 useres = 1
% 0.71/1.14 useparamod = 0
% 0.71/1.14 useeqrefl = 0
% 0.71/1.14 useeqfact = 0
% 0.71/1.14 usefactor = 1
% 0.71/1.14 usesimpsplitting = 0
% 0.71/1.14 usesimpdemod = 0
% 0.71/1.14 usesimpres = 3
% 0.71/1.14
% 0.71/1.14 resimpinuse = 1000
% 0.71/1.14 resimpclauses = 20000
% 0.71/1.14 substype = standard
% 0.71/1.14 backwardsubs = 1
% 0.71/1.14 selectoldest = 5
% 0.71/1.14
% 0.71/1.14 litorderings [0] = split
% 0.71/1.14 litorderings [1] = liftord
% 0.71/1.14
% 0.71/1.14 termordering = none
% 0.71/1.14
% 0.71/1.14 litapriori = 1
% 0.71/1.14 termapriori = 0
% 0.71/1.14 litaposteriori = 0
% 0.71/1.14 termaposteriori = 0
% 0.71/1.14 demodaposteriori = 0
% 0.71/1.14 ordereqreflfact = 0
% 0.71/1.14
% 0.71/1.14 litselect = none
% 0.71/1.14
% 0.71/1.14 maxweight = 15
% 0.71/1.14 maxdepth = 30000
% 0.71/1.14 maxlength = 115
% 0.71/1.14 maxnrvars = 195
% 0.71/1.14 excuselevel = 1
% 0.71/1.14 increasemaxweight = 1
% 0.71/1.14
% 0.71/1.14 maxselected = 10000000
% 0.71/1.14 maxnrclauses = 10000000
% 0.71/1.14
% 0.71/1.14 showgenerated = 0
% 0.71/1.14 showkept = 0
% 0.71/1.14 showselected = 0
% 0.71/1.14 showdeleted = 0
% 0.71/1.14 showresimp = 1
% 0.71/1.14 showstatus = 2000
% 0.71/1.14
% 0.71/1.14 prologoutput = 0
% 0.71/1.14 nrgoals = 5000000
% 0.71/1.14 totalproof = 1
% 0.71/1.14
% 0.71/1.14 Symbols occurring in the translation:
% 0.71/1.14
% 0.71/1.14 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.71/1.14 . [1, 2] (w:1, o:25, a:1, s:1, b:0),
% 0.71/1.14 ! [4, 1] (w:0, o:18, a:1, s:1, b:0),
% 0.71/1.14 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.71/1.14 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.71/1.14 distinct_points [36, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.71/1.14 distinct_lines [37, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.71/1.14 convergent_lines [38, 2] (w:1, o:49, a:1, s:1, b:0),
% 0.71/1.14 line_connecting [41, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.71/1.14 apart_point_and_line [42, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.71/1.14 intersection_point [43, 2] (w:1, o:54, a:1, s:1, b:0),
% 0.71/1.14 parallel_through_point [46, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.71/1.14 unorthogonal_lines [49, 2] (w:1, o:58, a:1, s:1, b:0),
% 0.71/1.14 orthogonal_through_point [52, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.71/1.14 point [54, 1] (w:1, o:23, a:1, s:1, b:0),
% 0.71/1.14 line [55, 1] (w:1, o:24, a:1, s:1, b:0),
% 0.71/1.14 equal_points [56, 2] (w:1, o:59, a:1, s:1, b:0),
% 0.71/1.14 equal_lines [57, 2] (w:1, o:60, a:1, s:1, b:0),
% 0.71/1.14 parallel_lines [58, 2] (w:1, o:61, a:1, s:1, b:0),
% 0.71/1.14 incident_point_and_line [59, 2] (w:1, o:62, a:1, s:1, b:0),
% 0.71/1.14 orthogonal_lines [60, 2] (w:1, o:56, a:1, s:1, b:0),
% 0.71/1.14 alpha1 [61, 2] (w:1, o:63, a:1, s:1, b:0),
% 0.71/1.14 alpha2 [62, 2] (w:1, o:64, a:1, s:1, b:0),
% 0.71/1.14 skol1 [63, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.71/1.14 skol2 [64, 0] (w:1, o:17, a:1, s:1, b:0).
% 0.71/1.14
% 0.71/1.14
% 0.71/1.14 Starting Search:
% 0.71/1.14
% 0.71/1.14 *** allocated 15000 integers for clauses
% 0.71/1.14 *** allocated 22500 integers for clauses
% 0.71/1.14 *** allocated 33750 integers for clauses
% 0.71/1.14 *** allocated 15000 integers for termspace/termends
% 0.71/1.14 *** allocated 50625 integers for clauses
% 0.71/1.14 Resimplifying inuse:
% 0.71/1.14 Done
% 0.71/1.14
% 0.71/1.14 *** allocated 22500 integers for termspace/termends
% 0.71/1.14 *** allocated 75937 integers for clauses
% 0.71/1.14 *** allocated 33750 integers for termspace/termends
% 0.71/1.14 *** allocated 113905 integers for clauses
% 0.71/1.14
% 0.71/1.14 Intermediate Status:
% 0.71/1.14 Generated: 24233
% 0.71/1.14 Kept: 2000
% 0.71/1.14 Inuse: 335
% 0.71/1.14 Deleted: 2
% 0.71/1.14 Deletedinuse: 2
% 0.71/1.14
% 0.71/1.14 Resimplifying inuse:
% 0.71/1.14 Done
% 0.71/1.14
% 0.71/1.14
% 0.71/1.14 Bliksems!, er is een bewijs:
% 0.71/1.14 % SZS status Theorem
% 0.71/1.14 % SZS output start Refutation
% 0.71/1.14
% 0.71/1.14 (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.71/1.14 (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ), convergent_lines( Y,
% 0.71/1.14 Z ), ! convergent_lines( X, Y ) }.
% 0.71/1.14 (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), unorthogonal_lines(
% 0.71/1.14 X, Y ) }.
% 0.71/1.14 (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 0.71/1.14 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 0.71/1.14 }.
% 0.71/1.14 (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! alpha1( X, Y ) }.
% 0.71/1.14 (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines( orthogonal_through_point
% 0.71/1.14 ( Y, X ), Y ) }.
% 0.71/1.14 (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ), unorthogonal_lines
% 0.71/1.14 ( Z, X ), unorthogonal_lines( Z, Y ) }.
% 0.71/1.14 (41) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), parallel_lines( X, Y
% 0.71/1.14 ) }.
% 0.71/1.14 (46) {G0,W7,D4,L1,V0,M1} I { ! parallel_lines( skol2,
% 0.71/1.14 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 0.71/1.14 ) ) }.
% 0.71/1.14 (62) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.71/1.14 convergent_lines( X, Y ) }.
% 0.71/1.14 (69) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 0.71/1.14 orthogonal_through_point( X, Y ), X ) }.
% 0.71/1.14 (71) {G2,W8,D3,L2,V3,M2} R(69,5) { convergent_lines( X, Z ),
% 0.71/1.14 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.71/1.14 (77) {G1,W7,D4,L1,V0,M1} R(46,41) { convergent_lines( skol2,
% 0.71/1.14 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 0.71/1.14 ) ) }.
% 0.71/1.14 (104) {G2,W7,D4,L1,V0,M1} R(77,62) { convergent_lines(
% 0.71/1.14 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 0.71/1.14 ), skol2 ) }.
% 0.71/1.14 (108) {G3,W8,D3,L2,V3,M2} R(71,62) { convergent_lines( Z, X ),
% 0.71/1.14 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.71/1.14 (150) {G4,W8,D3,L2,V3,M2} R(108,62) { convergent_lines( X,
% 0.71/1.14 orthogonal_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 0.71/1.14 (200) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y ),
% 0.71/1.14 convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 0.71/1.14 unorthogonal_lines( Y, Z ) }.
% 0.71/1.14 (312) {G1,W8,D3,L2,V3,M1} R(31,23) { ! convergent_lines( X, Y ),
% 0.71/1.14 unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 0.71/1.14 (2054) {G5,W8,D3,L2,V3,M1} R(200,23);r(150) { convergent_lines( X, Y ), !
% 0.71/1.14 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 0.71/1.14 (2061) {G6,W10,D3,L2,V4,M2} R(2054,312) { ! convergent_lines(
% 0.71/1.14 orthogonal_through_point( Z, T ), X ), convergent_lines(
% 0.71/1.14 orthogonal_through_point( X, Y ), Z ) }.
% 0.71/1.14 (2234) {G7,W7,D3,L1,V1,M1} R(2061,104) { convergent_lines(
% 0.71/1.14 orthogonal_through_point( skol2, X ), orthogonal_through_point( skol2,
% 0.71/1.14 skol1 ) ) }.
% 0.71/1.14 (2239) {G7,W7,D4,L1,V3,M1} R(2061,2) { ! convergent_lines(
% 0.71/1.14 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 0.71/1.14 (2242) {G8,W0,D0,L0,V0,M0} R(2234,2061);r(2239) { }.
% 0.71/1.14
% 0.71/1.14
% 0.71/1.14 % SZS output end Refutation
% 0.71/1.14 found a proof!
% 0.71/1.14
% 0.71/1.14
% 0.71/1.14 Unprocessed initial clauses:
% 0.71/1.14
% 0.71/1.14 (2244) {G0,W3,D2,L1,V1,M1} { ! distinct_points( X, X ) }.
% 0.71/1.14 (2245) {G0,W3,D2,L1,V1,M1} { ! distinct_lines( X, X ) }.
% 0.71/1.14 (2246) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 0.71/1.14 (2247) {G0,W9,D2,L3,V3,M3} { ! distinct_points( X, Y ), distinct_points( X
% 0.71/1.14 , Z ), distinct_points( Y, Z ) }.
% 0.71/1.14 (2248) {G0,W9,D2,L3,V3,M3} { ! distinct_lines( X, Y ), distinct_lines( X,
% 0.71/1.14 Z ), distinct_lines( Y, Z ) }.
% 0.71/1.14 (2249) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), convergent_lines
% 0.71/1.14 ( X, Z ), convergent_lines( Y, Z ) }.
% 0.71/1.14 (2250) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.71/1.14 apart_point_and_line( X, line_connecting( X, Y ) ) }.
% 0.71/1.14 (2251) {G0,W8,D3,L2,V2,M2} { ! distinct_points( X, Y ), !
% 0.71/1.14 apart_point_and_line( Y, line_connecting( X, Y ) ) }.
% 0.71/1.14 (2252) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 0.71/1.14 apart_point_and_line( intersection_point( X, Y ), X ) }.
% 0.71/1.14 (2253) {G0,W8,D3,L2,V2,M2} { ! convergent_lines( X, Y ), !
% 0.71/1.14 apart_point_and_line( intersection_point( X, Y ), Y ) }.
% 0.71/1.14 (2254) {G0,W18,D2,L6,V4,M6} { ! distinct_points( X, Y ), ! distinct_lines
% 0.71/1.14 ( Z, T ), apart_point_and_line( X, Z ), apart_point_and_line( X, T ),
% 0.71/1.14 apart_point_and_line( Y, Z ), apart_point_and_line( Y, T ) }.
% 0.71/1.14 (2255) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 0.71/1.14 distinct_points( X, Z ), apart_point_and_line( Z, Y ) }.
% 0.71/1.14 (2256) {G0,W9,D2,L3,V3,M3} { ! apart_point_and_line( X, Y ),
% 0.71/1.14 distinct_lines( Y, Z ), apart_point_and_line( X, Z ) }.
% 0.71/1.14 (2257) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ), distinct_lines( Y
% 0.71/1.14 , Z ), convergent_lines( X, Z ) }.
% 0.71/1.14 (2258) {G0,W6,D2,L2,V2,M2} { ! distinct_lines( X, Y ), convergent_lines( X
% 0.71/1.14 , Y ) }.
% 0.71/1.14 (2259) {G0,W5,D3,L1,V2,M1} { ! convergent_lines( parallel_through_point( Y
% 0.71/1.14 , X ), Y ) }.
% 0.71/1.14 (2260) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.71/1.14 parallel_through_point( Y, X ) ) }.
% 0.71/1.14 (2261) {G0,W12,D2,L4,V3,M4} { ! distinct_lines( X, Y ),
% 0.71/1.14 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 0.71/1.14 convergent_lines( X, Y ) }.
% 0.71/1.14 (2262) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines
% 0.71/1.14 ( X, Y ) }.
% 0.71/1.14 (2263) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.71/1.14 unorthogonal_lines( X, Y ), alpha1( X, Z ), convergent_lines( Y, Z ) }.
% 0.71/1.14 (2264) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.71/1.14 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 0.71/1.14 }.
% 0.71/1.14 (2265) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines( X, Y )
% 0.71/1.14 }.
% 0.71/1.14 (2266) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), unorthogonal_lines( X, Y )
% 0.71/1.14 }.
% 0.71/1.14 (2267) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( X, Y ), !
% 0.71/1.14 unorthogonal_lines( X, Y ), alpha1( X, Y ) }.
% 0.71/1.14 (2268) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines(
% 0.71/1.14 orthogonal_through_point( Y, X ), Y ) }.
% 0.71/1.14 (2269) {G0,W5,D3,L1,V2,M1} { ! apart_point_and_line( X,
% 0.71/1.14 orthogonal_through_point( Y, X ) ) }.
% 0.71/1.14 (2270) {G0,W15,D2,L5,V4,M5} { ! distinct_lines( X, Y ),
% 0.71/1.14 apart_point_and_line( Z, X ), apart_point_and_line( Z, Y ),
% 0.71/1.14 unorthogonal_lines( X, T ), unorthogonal_lines( Y, T ) }.
% 0.71/1.14 (2271) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), unorthogonal_lines
% 0.71/1.14 ( X, Y ) }.
% 0.71/1.14 (2272) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), convergent_lines( Z, Y ), !
% 0.71/1.14 convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.71/1.14 (2273) {G0,W12,D2,L4,V3,M4} { alpha2( X, Z ), unorthogonal_lines( Z, Y ),
% 0.71/1.14 ! convergent_lines( X, Y ), ! unorthogonal_lines( X, Y ) }.
% 0.71/1.14 (2274) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), convergent_lines( Y, X )
% 0.71/1.14 }.
% 0.71/1.14 (2275) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), unorthogonal_lines( Y, X )
% 0.71/1.14 }.
% 0.71/1.14 (2276) {G0,W9,D2,L3,V2,M3} { ! convergent_lines( Y, X ), !
% 0.71/1.14 unorthogonal_lines( Y, X ), alpha2( X, Y ) }.
% 0.71/1.14 (2277) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ),
% 0.71/1.14 unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 0.71/1.14 (2278) {G0,W11,D3,L4,V2,M4} { ! point( X ), ! point( Y ), !
% 0.71/1.14 distinct_points( X, Y ), line( line_connecting( X, Y ) ) }.
% 0.71/1.14 (2279) {G0,W11,D3,L4,V2,M4} { ! line( X ), ! line( Y ), ! convergent_lines
% 0.71/1.14 ( X, Y ), point( intersection_point( X, Y ) ) }.
% 0.71/1.14 (2280) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 0.71/1.14 parallel_through_point( X, Y ) ) }.
% 0.71/1.14 (2281) {G0,W8,D3,L3,V2,M3} { ! line( X ), ! point( Y ), line(
% 0.71/1.14 orthogonal_through_point( X, Y ) ) }.
% 0.71/1.14 (2282) {G0,W6,D2,L2,V2,M2} { ! equal_points( X, Y ), ! distinct_points( X
% 0.71/1.14 , Y ) }.
% 0.71/1.14 (2283) {G0,W6,D2,L2,V2,M2} { distinct_points( X, Y ), equal_points( X, Y )
% 0.71/1.14 }.
% 0.71/1.14 (2284) {G0,W6,D2,L2,V2,M2} { ! equal_lines( X, Y ), ! distinct_lines( X, Y
% 0.71/1.14 ) }.
% 0.71/1.14 (2285) {G0,W6,D2,L2,V2,M2} { distinct_lines( X, Y ), equal_lines( X, Y )
% 0.71/1.14 }.
% 0.71/1.14 (2286) {G0,W6,D2,L2,V2,M2} { ! parallel_lines( X, Y ), ! convergent_lines
% 0.71/1.14 ( X, Y ) }.
% 0.71/1.14 (2287) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ), parallel_lines( X,
% 0.71/1.14 Y ) }.
% 0.71/1.14 (2288) {G0,W6,D2,L2,V2,M2} { ! incident_point_and_line( X, Y ), !
% 0.71/1.14 apart_point_and_line( X, Y ) }.
% 0.71/1.14 (2289) {G0,W6,D2,L2,V2,M2} { apart_point_and_line( X, Y ),
% 0.71/1.14 incident_point_and_line( X, Y ) }.
% 0.71/1.14 (2290) {G0,W6,D2,L2,V2,M2} { ! orthogonal_lines( X, Y ), !
% 0.71/1.14 unorthogonal_lines( X, Y ) }.
% 0.71/1.14 (2291) {G0,W6,D2,L2,V2,M2} { unorthogonal_lines( X, Y ), orthogonal_lines
% 0.71/1.14 ( X, Y ) }.
% 0.71/1.14 (2292) {G0,W7,D4,L1,V0,M1} { ! parallel_lines( skol2,
% 0.71/1.14 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 0.71/1.14 ) ) }.
% 0.71/1.14
% 0.71/1.14
% 0.71/1.14 Total Proof:
% 0.71/1.14
% 0.71/1.14 subsumption: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.71/1.14 parent0: (2246) {G0,W3,D2,L1,V1,M1} { ! convergent_lines( X, X ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := X
% 0.71/1.14 end
% 0.71/1.14 permutation0:
% 0.71/1.14 0 ==> 0
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 subsumption: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 0.71/1.14 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.71/1.14 parent0: (2249) {G0,W9,D2,L3,V3,M3} { ! convergent_lines( X, Y ),
% 0.71/1.14 convergent_lines( X, Z ), convergent_lines( Y, Z ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := X
% 0.71/1.14 Y := Y
% 0.71/1.14 Z := Z
% 0.71/1.14 end
% 0.71/1.14 permutation0:
% 0.71/1.14 0 ==> 2
% 0.71/1.14 1 ==> 0
% 0.71/1.14 2 ==> 1
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 subsumption: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 0.71/1.14 unorthogonal_lines( X, Y ) }.
% 0.71/1.14 parent0: (2262) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ),
% 0.71/1.14 unorthogonal_lines( X, Y ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := X
% 0.71/1.14 Y := Y
% 0.71/1.14 end
% 0.71/1.14 permutation0:
% 0.71/1.14 0 ==> 0
% 0.71/1.14 1 ==> 1
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 subsumption: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 0.71/1.14 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 0.71/1.14 }.
% 0.71/1.14 parent0: (2264) {G0,W12,D2,L4,V3,M4} { ! convergent_lines( X, Y ), !
% 0.71/1.14 unorthogonal_lines( X, Y ), alpha1( X, Z ), unorthogonal_lines( Y, Z )
% 0.71/1.14 }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := X
% 0.71/1.14 Y := Y
% 0.71/1.14 Z := Z
% 0.71/1.14 end
% 0.71/1.14 permutation0:
% 0.71/1.14 0 ==> 0
% 0.71/1.14 1 ==> 1
% 0.71/1.14 2 ==> 3
% 0.71/1.14 3 ==> 2
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 *** allocated 50625 integers for termspace/termends
% 0.71/1.14 subsumption: (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), !
% 0.71/1.14 alpha1( X, Y ) }.
% 0.71/1.14 parent0: (2265) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), convergent_lines(
% 0.71/1.14 X, Y ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := X
% 0.71/1.14 Y := Y
% 0.71/1.14 end
% 0.71/1.14 permutation0:
% 0.71/1.14 0 ==> 1
% 0.71/1.14 1 ==> 0
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 subsumption: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 0.71/1.14 orthogonal_through_point( Y, X ), Y ) }.
% 0.71/1.14 parent0: (2268) {G0,W5,D3,L1,V2,M1} { ! unorthogonal_lines(
% 0.71/1.14 orthogonal_through_point( Y, X ), Y ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := X
% 0.71/1.14 Y := Y
% 0.71/1.14 end
% 0.71/1.14 permutation0:
% 0.71/1.14 0 ==> 0
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 subsumption: (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ),
% 0.71/1.14 unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ) }.
% 0.71/1.14 parent0: (2277) {G0,W9,D2,L3,V3,M3} { unorthogonal_lines( Z, X ),
% 0.71/1.14 unorthogonal_lines( Z, Y ), ! convergent_lines( X, Y ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := X
% 0.71/1.14 Y := Y
% 0.71/1.14 Z := Z
% 0.71/1.14 end
% 0.71/1.14 permutation0:
% 0.71/1.14 0 ==> 1
% 0.71/1.14 1 ==> 2
% 0.71/1.14 2 ==> 0
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 subsumption: (41) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 0.71/1.14 parallel_lines( X, Y ) }.
% 0.71/1.14 parent0: (2287) {G0,W6,D2,L2,V2,M2} { convergent_lines( X, Y ),
% 0.71/1.14 parallel_lines( X, Y ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := X
% 0.71/1.14 Y := Y
% 0.71/1.14 end
% 0.71/1.14 permutation0:
% 0.71/1.14 0 ==> 0
% 0.71/1.14 1 ==> 1
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 subsumption: (46) {G0,W7,D4,L1,V0,M1} I { ! parallel_lines( skol2,
% 0.71/1.14 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 0.71/1.14 ) ) }.
% 0.71/1.14 parent0: (2292) {G0,W7,D4,L1,V0,M1} { ! parallel_lines( skol2,
% 0.71/1.14 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 0.71/1.14 ) ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 end
% 0.71/1.14 permutation0:
% 0.71/1.14 0 ==> 0
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 resolution: (2379) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 0.71/1.14 convergent_lines( X, Y ) }.
% 0.71/1.14 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.71/1.14 parent1[0]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 0.71/1.14 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := X
% 0.71/1.14 end
% 0.71/1.14 substitution1:
% 0.71/1.14 X := X
% 0.71/1.14 Y := Y
% 0.71/1.14 Z := X
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 subsumption: (62) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.71/1.14 convergent_lines( X, Y ) }.
% 0.71/1.14 parent0: (2379) {G1,W6,D2,L2,V2,M2} { convergent_lines( Y, X ), !
% 0.71/1.14 convergent_lines( X, Y ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := Y
% 0.71/1.14 Y := X
% 0.71/1.14 end
% 0.71/1.14 permutation0:
% 0.71/1.14 0 ==> 1
% 0.71/1.14 1 ==> 0
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 resolution: (2381) {G1,W5,D3,L1,V2,M1} { convergent_lines(
% 0.71/1.14 orthogonal_through_point( X, Y ), X ) }.
% 0.71/1.14 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 0.71/1.14 orthogonal_through_point( Y, X ), Y ) }.
% 0.71/1.14 parent1[1]: (17) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 0.71/1.14 unorthogonal_lines( X, Y ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := Y
% 0.71/1.14 Y := X
% 0.71/1.14 end
% 0.71/1.14 substitution1:
% 0.71/1.14 X := orthogonal_through_point( X, Y )
% 0.71/1.14 Y := X
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 subsumption: (69) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 0.71/1.14 orthogonal_through_point( X, Y ), X ) }.
% 0.71/1.14 parent0: (2381) {G1,W5,D3,L1,V2,M1} { convergent_lines(
% 0.71/1.14 orthogonal_through_point( X, Y ), X ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := X
% 0.71/1.14 Y := Y
% 0.71/1.14 end
% 0.71/1.14 permutation0:
% 0.71/1.14 0 ==> 0
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 resolution: (2382) {G1,W8,D3,L2,V3,M2} { convergent_lines(
% 0.71/1.14 orthogonal_through_point( X, Y ), Z ), convergent_lines( X, Z ) }.
% 0.71/1.14 parent0[2]: (5) {G0,W9,D2,L3,V3,M3} I { convergent_lines( X, Z ),
% 0.71/1.14 convergent_lines( Y, Z ), ! convergent_lines( X, Y ) }.
% 0.71/1.14 parent1[0]: (69) {G1,W5,D3,L1,V2,M1} R(17,23) { convergent_lines(
% 0.71/1.14 orthogonal_through_point( X, Y ), X ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := orthogonal_through_point( X, Y )
% 0.71/1.14 Y := X
% 0.71/1.14 Z := Z
% 0.71/1.14 end
% 0.71/1.14 substitution1:
% 0.71/1.14 X := X
% 0.71/1.14 Y := Y
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 subsumption: (71) {G2,W8,D3,L2,V3,M2} R(69,5) { convergent_lines( X, Z ),
% 0.71/1.14 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.71/1.14 parent0: (2382) {G1,W8,D3,L2,V3,M2} { convergent_lines(
% 0.71/1.14 orthogonal_through_point( X, Y ), Z ), convergent_lines( X, Z ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := X
% 0.71/1.14 Y := Y
% 0.71/1.14 Z := Z
% 0.71/1.14 end
% 0.71/1.14 permutation0:
% 0.71/1.14 0 ==> 1
% 0.71/1.14 1 ==> 0
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 resolution: (2383) {G1,W7,D4,L1,V0,M1} { convergent_lines( skol2,
% 0.71/1.14 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 0.71/1.14 ) ) }.
% 0.71/1.14 parent0[0]: (46) {G0,W7,D4,L1,V0,M1} I { ! parallel_lines( skol2,
% 0.71/1.14 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 0.71/1.14 ) ) }.
% 0.71/1.14 parent1[1]: (41) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ),
% 0.71/1.14 parallel_lines( X, Y ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 end
% 0.71/1.14 substitution1:
% 0.71/1.14 X := skol2
% 0.71/1.14 Y := orthogonal_through_point( orthogonal_through_point( skol2, skol1 )
% 0.71/1.14 , skol1 )
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 subsumption: (77) {G1,W7,D4,L1,V0,M1} R(46,41) { convergent_lines( skol2,
% 0.71/1.14 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 0.71/1.14 ) ) }.
% 0.71/1.14 parent0: (2383) {G1,W7,D4,L1,V0,M1} { convergent_lines( skol2,
% 0.71/1.14 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 0.71/1.14 ) ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 end
% 0.71/1.14 permutation0:
% 0.71/1.14 0 ==> 0
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 resolution: (2384) {G2,W7,D4,L1,V0,M1} { convergent_lines(
% 0.71/1.14 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 0.71/1.14 ), skol2 ) }.
% 0.71/1.14 parent0[0]: (62) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.71/1.14 convergent_lines( X, Y ) }.
% 0.71/1.14 parent1[0]: (77) {G1,W7,D4,L1,V0,M1} R(46,41) { convergent_lines( skol2,
% 0.71/1.14 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 0.71/1.14 ) ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := orthogonal_through_point( orthogonal_through_point( skol2, skol1 )
% 0.71/1.14 , skol1 )
% 0.71/1.14 Y := skol2
% 0.71/1.14 end
% 0.71/1.14 substitution1:
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 subsumption: (104) {G2,W7,D4,L1,V0,M1} R(77,62) { convergent_lines(
% 0.71/1.14 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 0.71/1.14 ), skol2 ) }.
% 0.71/1.14 parent0: (2384) {G2,W7,D4,L1,V0,M1} { convergent_lines(
% 0.71/1.14 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 0.71/1.14 ), skol2 ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 end
% 0.71/1.14 permutation0:
% 0.71/1.14 0 ==> 0
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 resolution: (2385) {G2,W8,D3,L2,V3,M2} { convergent_lines( Y, X ),
% 0.71/1.14 convergent_lines( orthogonal_through_point( X, Z ), Y ) }.
% 0.71/1.14 parent0[0]: (62) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.71/1.14 convergent_lines( X, Y ) }.
% 0.71/1.14 parent1[0]: (71) {G2,W8,D3,L2,V3,M2} R(69,5) { convergent_lines( X, Z ),
% 0.71/1.14 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := Y
% 0.71/1.14 Y := X
% 0.71/1.14 end
% 0.71/1.14 substitution1:
% 0.71/1.14 X := X
% 0.71/1.14 Y := Z
% 0.71/1.14 Z := Y
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 subsumption: (108) {G3,W8,D3,L2,V3,M2} R(71,62) { convergent_lines( Z, X )
% 0.71/1.14 , convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.71/1.14 parent0: (2385) {G2,W8,D3,L2,V3,M2} { convergent_lines( Y, X ),
% 0.71/1.14 convergent_lines( orthogonal_through_point( X, Z ), Y ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := X
% 0.71/1.14 Y := Z
% 0.71/1.14 Z := Y
% 0.71/1.14 end
% 0.71/1.14 permutation0:
% 0.71/1.14 0 ==> 0
% 0.71/1.14 1 ==> 1
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 resolution: (2388) {G2,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 0.71/1.14 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ) }.
% 0.71/1.14 parent0[0]: (62) {G1,W6,D2,L2,V2,M2} R(5,2) { ! convergent_lines( Y, X ),
% 0.71/1.14 convergent_lines( X, Y ) }.
% 0.71/1.14 parent1[1]: (108) {G3,W8,D3,L2,V3,M2} R(71,62) { convergent_lines( Z, X ),
% 0.71/1.14 convergent_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := Z
% 0.71/1.14 Y := orthogonal_through_point( X, Y )
% 0.71/1.14 end
% 0.71/1.14 substitution1:
% 0.71/1.14 X := X
% 0.71/1.14 Y := Y
% 0.71/1.14 Z := Z
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 subsumption: (150) {G4,W8,D3,L2,V3,M2} R(108,62) { convergent_lines( X,
% 0.71/1.14 orthogonal_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 0.71/1.14 parent0: (2388) {G2,W8,D3,L2,V3,M2} { convergent_lines( Z,
% 0.71/1.14 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := Y
% 0.71/1.14 Y := Z
% 0.71/1.14 Z := X
% 0.71/1.14 end
% 0.71/1.14 permutation0:
% 0.71/1.14 0 ==> 0
% 0.71/1.14 1 ==> 1
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 resolution: (2390) {G1,W12,D2,L4,V3,M4} { convergent_lines( X, Y ), !
% 0.71/1.14 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ),
% 0.71/1.14 unorthogonal_lines( Z, Y ) }.
% 0.71/1.14 parent0[1]: (20) {G0,W6,D2,L2,V2,M1} I { convergent_lines( X, Y ), ! alpha1
% 0.71/1.14 ( X, Y ) }.
% 0.71/1.14 parent1[3]: (19) {G0,W12,D2,L4,V3,M1} I { ! convergent_lines( X, Y ), !
% 0.71/1.14 unorthogonal_lines( X, Y ), unorthogonal_lines( Y, Z ), alpha1( X, Z )
% 0.71/1.14 }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := X
% 0.71/1.14 Y := Y
% 0.71/1.14 end
% 0.71/1.14 substitution1:
% 0.71/1.14 X := X
% 0.71/1.14 Y := Z
% 0.71/1.14 Z := Y
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 subsumption: (200) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y
% 0.71/1.14 ), convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 0.71/1.14 unorthogonal_lines( Y, Z ) }.
% 0.71/1.14 parent0: (2390) {G1,W12,D2,L4,V3,M4} { convergent_lines( X, Y ), !
% 0.71/1.14 convergent_lines( X, Z ), ! unorthogonal_lines( X, Z ),
% 0.71/1.14 unorthogonal_lines( Z, Y ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := X
% 0.71/1.14 Y := Z
% 0.71/1.14 Z := Y
% 0.71/1.14 end
% 0.71/1.14 permutation0:
% 0.71/1.14 0 ==> 1
% 0.71/1.14 1 ==> 0
% 0.71/1.14 2 ==> 2
% 0.71/1.14 3 ==> 3
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 resolution: (2392) {G1,W8,D3,L2,V3,M2} { ! convergent_lines( Z, X ),
% 0.71/1.14 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.71/1.14 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 0.71/1.14 orthogonal_through_point( Y, X ), Y ) }.
% 0.71/1.14 parent1[2]: (31) {G0,W9,D2,L3,V3,M2} I { ! convergent_lines( X, Y ),
% 0.71/1.14 unorthogonal_lines( Z, X ), unorthogonal_lines( Z, Y ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := Y
% 0.71/1.14 Y := X
% 0.71/1.14 end
% 0.71/1.14 substitution1:
% 0.71/1.14 X := Z
% 0.71/1.14 Y := X
% 0.71/1.14 Z := orthogonal_through_point( X, Y )
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 subsumption: (312) {G1,W8,D3,L2,V3,M1} R(31,23) { ! convergent_lines( X, Y
% 0.71/1.14 ), unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 0.71/1.14 parent0: (2392) {G1,W8,D3,L2,V3,M2} { ! convergent_lines( Z, X ),
% 0.71/1.14 unorthogonal_lines( orthogonal_through_point( X, Y ), Z ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := Y
% 0.71/1.14 Y := Z
% 0.71/1.14 Z := X
% 0.71/1.14 end
% 0.71/1.14 permutation0:
% 0.71/1.14 0 ==> 0
% 0.71/1.14 1 ==> 1
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 resolution: (2393) {G1,W13,D3,L3,V3,M3} { ! convergent_lines( Z,
% 0.71/1.14 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ), !
% 0.71/1.14 unorthogonal_lines( Z, orthogonal_through_point( X, Y ) ) }.
% 0.71/1.14 parent0[0]: (23) {G0,W5,D3,L1,V2,M1} I { ! unorthogonal_lines(
% 0.71/1.14 orthogonal_through_point( Y, X ), Y ) }.
% 0.71/1.14 parent1[3]: (200) {G1,W12,D2,L4,V3,M2} R(19,20) { ! convergent_lines( X, Y
% 0.71/1.14 ), convergent_lines( X, Z ), ! unorthogonal_lines( X, Y ),
% 0.71/1.14 unorthogonal_lines( Y, Z ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := Y
% 0.71/1.14 Y := X
% 0.71/1.14 end
% 0.71/1.14 substitution1:
% 0.71/1.14 X := Z
% 0.71/1.14 Y := orthogonal_through_point( X, Y )
% 0.71/1.14 Z := X
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 resolution: (2394) {G2,W11,D3,L3,V3,M3} { convergent_lines( X, Y ), !
% 0.71/1.14 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ),
% 0.71/1.14 convergent_lines( X, Y ) }.
% 0.71/1.14 parent0[0]: (2393) {G1,W13,D3,L3,V3,M3} { ! convergent_lines( Z,
% 0.71/1.14 orthogonal_through_point( X, Y ) ), convergent_lines( Z, X ), !
% 0.71/1.14 unorthogonal_lines( Z, orthogonal_through_point( X, Y ) ) }.
% 0.71/1.14 parent1[0]: (150) {G4,W8,D3,L2,V3,M2} R(108,62) { convergent_lines( X,
% 0.71/1.14 orthogonal_through_point( Y, Z ) ), convergent_lines( X, Y ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := Y
% 0.71/1.14 Y := Z
% 0.71/1.14 Z := X
% 0.71/1.14 end
% 0.71/1.14 substitution1:
% 0.71/1.14 X := X
% 0.71/1.14 Y := Y
% 0.71/1.14 Z := Z
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 factor: (2395) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 0.71/1.14 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 0.71/1.14 parent0[0, 2]: (2394) {G2,W11,D3,L3,V3,M3} { convergent_lines( X, Y ), !
% 0.71/1.14 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ),
% 0.71/1.14 convergent_lines( X, Y ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := X
% 0.71/1.14 Y := Y
% 0.71/1.14 Z := Z
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 subsumption: (2054) {G5,W8,D3,L2,V3,M1} R(200,23);r(150) { convergent_lines
% 0.71/1.14 ( X, Y ), ! unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 0.71/1.14 parent0: (2395) {G2,W8,D3,L2,V3,M2} { convergent_lines( X, Y ), !
% 0.71/1.14 unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := X
% 0.71/1.14 Y := Y
% 0.71/1.14 Z := Z
% 0.71/1.14 end
% 0.71/1.14 permutation0:
% 0.71/1.14 0 ==> 0
% 0.71/1.14 1 ==> 1
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 resolution: (2396) {G2,W10,D3,L2,V4,M2} { convergent_lines(
% 0.71/1.14 orthogonal_through_point( X, Y ), Z ), ! convergent_lines(
% 0.71/1.14 orthogonal_through_point( Z, T ), X ) }.
% 0.71/1.14 parent0[1]: (2054) {G5,W8,D3,L2,V3,M1} R(200,23);r(150) { convergent_lines
% 0.71/1.14 ( X, Y ), ! unorthogonal_lines( X, orthogonal_through_point( Y, Z ) ) }.
% 0.71/1.14 parent1[1]: (312) {G1,W8,D3,L2,V3,M1} R(31,23) { ! convergent_lines( X, Y )
% 0.71/1.14 , unorthogonal_lines( orthogonal_through_point( Y, Z ), X ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := orthogonal_through_point( X, Y )
% 0.71/1.14 Y := Z
% 0.71/1.14 Z := T
% 0.71/1.14 end
% 0.71/1.14 substitution1:
% 0.71/1.14 X := orthogonal_through_point( Z, T )
% 0.71/1.14 Y := X
% 0.71/1.14 Z := Y
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 subsumption: (2061) {G6,W10,D3,L2,V4,M2} R(2054,312) { ! convergent_lines(
% 0.71/1.14 orthogonal_through_point( Z, T ), X ), convergent_lines(
% 0.71/1.14 orthogonal_through_point( X, Y ), Z ) }.
% 0.71/1.14 parent0: (2396) {G2,W10,D3,L2,V4,M2} { convergent_lines(
% 0.71/1.14 orthogonal_through_point( X, Y ), Z ), ! convergent_lines(
% 0.71/1.14 orthogonal_through_point( Z, T ), X ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := X
% 0.71/1.14 Y := Y
% 0.71/1.14 Z := Z
% 0.71/1.14 T := T
% 0.71/1.14 end
% 0.71/1.14 permutation0:
% 0.71/1.14 0 ==> 1
% 0.71/1.14 1 ==> 0
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 resolution: (2397) {G3,W7,D3,L1,V1,M1} { convergent_lines(
% 0.71/1.14 orthogonal_through_point( skol2, X ), orthogonal_through_point( skol2,
% 0.71/1.14 skol1 ) ) }.
% 0.71/1.14 parent0[0]: (2061) {G6,W10,D3,L2,V4,M2} R(2054,312) { ! convergent_lines(
% 0.71/1.14 orthogonal_through_point( Z, T ), X ), convergent_lines(
% 0.71/1.14 orthogonal_through_point( X, Y ), Z ) }.
% 0.71/1.14 parent1[0]: (104) {G2,W7,D4,L1,V0,M1} R(77,62) { convergent_lines(
% 0.71/1.14 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), skol1
% 0.71/1.14 ), skol2 ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := skol2
% 0.71/1.14 Y := X
% 0.71/1.14 Z := orthogonal_through_point( skol2, skol1 )
% 0.71/1.14 T := skol1
% 0.71/1.14 end
% 0.71/1.14 substitution1:
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 subsumption: (2234) {G7,W7,D3,L1,V1,M1} R(2061,104) { convergent_lines(
% 0.71/1.14 orthogonal_through_point( skol2, X ), orthogonal_through_point( skol2,
% 0.71/1.14 skol1 ) ) }.
% 0.71/1.14 parent0: (2397) {G3,W7,D3,L1,V1,M1} { convergent_lines(
% 0.71/1.14 orthogonal_through_point( skol2, X ), orthogonal_through_point( skol2,
% 0.71/1.14 skol1 ) ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := X
% 0.71/1.14 end
% 0.71/1.14 permutation0:
% 0.71/1.14 0 ==> 0
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 resolution: (2398) {G1,W7,D4,L1,V3,M1} { ! convergent_lines(
% 0.71/1.14 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 0.71/1.14 parent0[0]: (2) {G0,W3,D2,L1,V1,M1} I { ! convergent_lines( X, X ) }.
% 0.71/1.14 parent1[1]: (2061) {G6,W10,D3,L2,V4,M2} R(2054,312) { ! convergent_lines(
% 0.71/1.14 orthogonal_through_point( Z, T ), X ), convergent_lines(
% 0.71/1.14 orthogonal_through_point( X, Y ), Z ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := orthogonal_through_point( X, Y )
% 0.71/1.14 end
% 0.71/1.14 substitution1:
% 0.71/1.14 X := X
% 0.71/1.14 Y := Y
% 0.71/1.14 Z := orthogonal_through_point( X, Y )
% 0.71/1.14 T := Z
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 subsumption: (2239) {G7,W7,D4,L1,V3,M1} R(2061,2) { ! convergent_lines(
% 0.71/1.14 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 0.71/1.14 parent0: (2398) {G1,W7,D4,L1,V3,M1} { ! convergent_lines(
% 0.71/1.14 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := X
% 0.71/1.14 Y := Y
% 0.71/1.14 Z := Z
% 0.71/1.14 end
% 0.71/1.14 permutation0:
% 0.71/1.14 0 ==> 0
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 resolution: (2399) {G7,W7,D4,L1,V1,M1} { convergent_lines(
% 0.71/1.14 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), Y ),
% 0.71/1.14 skol2 ) }.
% 0.71/1.14 parent0[0]: (2061) {G6,W10,D3,L2,V4,M2} R(2054,312) { ! convergent_lines(
% 0.71/1.14 orthogonal_through_point( Z, T ), X ), convergent_lines(
% 0.71/1.14 orthogonal_through_point( X, Y ), Z ) }.
% 0.71/1.14 parent1[0]: (2234) {G7,W7,D3,L1,V1,M1} R(2061,104) { convergent_lines(
% 0.71/1.14 orthogonal_through_point( skol2, X ), orthogonal_through_point( skol2,
% 0.71/1.14 skol1 ) ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := orthogonal_through_point( skol2, skol1 )
% 0.71/1.14 Y := Y
% 0.71/1.14 Z := skol2
% 0.71/1.14 T := X
% 0.71/1.14 end
% 0.71/1.14 substitution1:
% 0.71/1.14 X := X
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 resolution: (2400) {G8,W0,D0,L0,V0,M0} { }.
% 0.71/1.14 parent0[0]: (2239) {G7,W7,D4,L1,V3,M1} R(2061,2) { ! convergent_lines(
% 0.71/1.14 orthogonal_through_point( orthogonal_through_point( X, Y ), Z ), X ) }.
% 0.71/1.14 parent1[0]: (2399) {G7,W7,D4,L1,V1,M1} { convergent_lines(
% 0.71/1.14 orthogonal_through_point( orthogonal_through_point( skol2, skol1 ), Y ),
% 0.71/1.14 skol2 ) }.
% 0.71/1.14 substitution0:
% 0.71/1.14 X := skol2
% 0.71/1.14 Y := skol1
% 0.71/1.14 Z := X
% 0.71/1.14 end
% 0.71/1.14 substitution1:
% 0.71/1.14 X := Y
% 0.71/1.14 Y := X
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 subsumption: (2242) {G8,W0,D0,L0,V0,M0} R(2234,2061);r(2239) { }.
% 0.71/1.14 parent0: (2400) {G8,W0,D0,L0,V0,M0} { }.
% 0.71/1.14 substitution0:
% 0.71/1.14 end
% 0.71/1.14 permutation0:
% 0.71/1.14 end
% 0.71/1.14
% 0.71/1.14 Proof check complete!
% 0.71/1.14
% 0.71/1.14 Memory use:
% 0.71/1.14
% 0.71/1.14 space for terms: 32948
% 0.71/1.14 space for clauses: 92151
% 0.71/1.14
% 0.71/1.14
% 0.71/1.14 clauses generated: 24944
% 0.71/1.14 clauses kept: 2243
% 0.71/1.14 clauses selected: 350
% 0.71/1.14 clauses deleted: 2
% 0.71/1.14 clauses inuse deleted: 2
% 0.71/1.14
% 0.71/1.14 subsentry: 511548
% 0.71/1.14 literals s-matched: 236198
% 0.71/1.14 literals matched: 236150
% 0.71/1.14 full subsumption: 160293
% 0.71/1.14
% 0.71/1.14 checksum: 1527337373
% 0.71/1.14
% 0.71/1.14
% 0.71/1.14 Bliksem ended
%------------------------------------------------------------------------------